raattgift

This comment started as a short scribble ("I mostly agree", in essence) but I kept getting distracted, going away, coming back and adding more. It seems to have grown in length but not in focus.

I completely agree for cosmological spacetimes. I largely agree more generally, other than thinking one shouldn't be afraid of Landau-Lifshitz and company for fear of lack of "rigour", or even resorting to vectors[1] in appropriate circumstances. Everyone should already know doing so can be a footgun. If not, someone will call them out (reviewer 2 if unlucky).

That said, it's just a blog posting aimed at non-scientists. As I know you know, Carroll has well-regarded lecture notes and now a textbook [§3.5 in the lead up to eqn 3.92 is roughly the meat of the blog post, and for the sentence you picked out cf §3.8's discussion of the use of Killing's equation, around eqns 3.178 - 3.181, defining a total energy after slicing certain spacetimes (but not the cosmological one, of course)] for anyone who wants more "rigour". :-)

Another nice -- in fact, imho better, because of how it gets to eqn (3) [and the side comment in square brackets immediately after it -- it's not a gravitational statement!] -- blog entry covering similar territory is by Michael Weiss (the diagonalargument.com one) & John C Baez: https://math.ucr.edu/home/baez/physics/Relativity/GR/energy_... Cherry picking their support for the point you make: 'These pseudo-tensors have some rather strange properties. If you choose the "wrong" coordinates, they are non-zero even in flat empty spacetime. By another choice of coordinates, they can be made zero at any chosen point, even in a spacetime full of gravitational radiation. For these reasons, most physicists who work in general relativity do not believe the pseudo-tensors give a good local definition of energy density, although their integrals are sometimes useful as a measure of total energy.'

I will admit that your notion of "rigor" is unusual to see in strongly relativistic astrophysics (e.g. NS-NS GW 170817 literature), and practically unheard of in the low speed weak field limit. So what? Is using GEM's vectors there somehow wrong just because it's a pain to deal with relatively boosted frames?

I think you're wrong that 'Any way of defining "the energy of the whole universe" will involve what are called "pseudotensors"'. There are other approaches. More germane to astrophysics -- although this is perhaps arguing more with Weiss&Baez than you? -- there is lots of work on trying to define quasilocal energy without pseudotensors. See especially e.g. the first paragraph and endnote [1] of Brown & York 1993 PRD vol 47 iss 4 <https://harvest.aps.org/v2/journals/articles/10.1103/PhysRev...> (direct PDF). And now I should really make myself time to trawl through the recent relevant work of self-styled "mathematician who pretends to be a physicist", Steve McCormick <https://www.quasilocal.com/#section2>.

- --

[1] For fun: "Linear algebra is easy. Just remember [that] real numbers are vectors, polynomials are vectors, integrable functions are vectors, matrices are vectors, tensors are vectors, and so on. As I said, easy." @j_bertolotti lighting a fire https://twitter.com/j_bertolotti/status/1786407421755134325 And a golden reply, "All tensors are vectors. They're not in the same vector space as the vectors they're maps for, but a tensor product of vector spaces is another vector space, satisfying all the axioms." https://twitter.com/roystgnr/status/1786449834498511130

Here's something for you to think about.

Light from sources at cosmological distances is redshifted, and we have several excellent lines of evidence for that, notably https://en.wikipedia.org/wiki/Lyman-alpha_forest which clearly shows that the emitted light was redshifted progressively as it reached intervening clouds of hydrogen on its way to our spectrographs.

Energy is directly proportional to wavelength. For light, E = hf, where h is Planck's constant. It's inversely proportional to wavelength, E = (hc)/λ, where c is the speed of light and λ is the wavelength. Redshifting means longer wavelengths, so less energy at the point of detection compared to the point of emission.

Energy conservation is local. At large scales, photons lose energy. Where does it go?

After you've thought about that on your own for a bit, compare your thinking with working physical cosmologist Sean Carroll's blog entry https://www.preposterousuniverse.com/blog/2010/02/22/energy-...

The connection to what I wrote above is that General Relativity guarantees that at every single point in a general curved spacetime there is a small patch of (quasi-)static flat spacetime. That patch can be ultramicroscopic deep within a black hole, or very large (in human terms) in interplanetary space in our solar system. In that flat patch energy conservation holds, as Carroll described. Outside that patch, we can see light redshift or blueshift through spacetime; the same energy shifts happen to massive particles like cosmic ray electrons, protons and neutrinos, too. It also happens to gravitational waves.

Event horizons break time-reversal symmetry. Nothing comes back from the other side. Generically, in the presence of a relativistic quantum field (like the 17 in the standard model of particle physics), an event horizon radiates greybody radiation comparable to a blackbody with a temperature inversely proportional to the horizon area. To save words, we just use that temperature (and go back to a calculation of the exact spectrum when greater accuracy is required). Black hole event horizons are really cold. Cosmological event horizons are ridiculously cold. And really it's the apparent horizon that has a measurable temperature. There may not be an event horizon in finite time, but in many circumstances the apparent horizon is indistinguishable by experiment. We have evidence of matter crossing to the other side of these horizons (e.g. from tidal disruption events and black hole/neutron star collisions); we have decent upper limits on horizon temperatures for a small handful of black hole horizons. (And someday we will have precision laboratory evidence of Unruh event horizon temperatures).

If the universe undergoes recollapse, black holes will tend to merge into ever bigger black holes as galaxy clusters freely-fall closer together (and then interact with each other, merging into gargantuan elliptical things with silly large velocity dispersions generating all sorts of collision & merger opportunities). So you need some unknown extra step to undo the time-reversal invariance violation of black hole horizons. Have any ideas?

The bright side is that black holes hold so much entropy that you aren't in any danger of violating the second law of thermodynamics via recollapse, unless your idea does that accidentally. The entropy is easy to see in a Boltzmann sense. Given the "no hair" conjecture, a black hole is fully described by a small number of parameters. Those parameters are a macrostate. A microstate is a configuration of things that fell into the black hole imparting its mass and spin and charge(s)). Entropy is proportional to the log of all the possible microstates for that macrostate. As more matter goes into a black hole, its entropy skyrockets. (The increase in BH entropy absolutely dwarfs the decrease in vacuum entropy; since hard vacuum is a macrostate, and every reasonable volume of hard vacuum is totally substitutable for every other similar volume of hard vacuum, there's a lot of entropy there too. As we fill the vacuum with ejected stars, radiation, high-metallicity dust, and so on as we squash galaxy clusters together during recollapse, that's a loss of entropy. But still nowhere near as low an entropy as the original cold gas clouds that were around after the cosmic microwave background formed. So your idea that recollapse means low entropy is on shaky ground, especially if you are taking your "binary counter ticks back to zero" idea seriously. You can take some comfort that lots of very smart people who can do the maths and have decent physical intuitions (Penrose comes to mind) have struggled with entropy in a cyclic cosmology.

Finally, the Hubble tension at its very strongest changes the age of the the oldest galaxies from almost 14 billion years to almost double that, not whether it the universe is expanding faster now than it was between one and four billion years ago. It's not something on which you want to rest a theory of cosmic recollapse.

You're not all that far from describing dark energy.

Gravitational attraction tends to cause the trajectories of freely-falling ("floating in empty space") masses to converge. Dark energy tends to cause the trajectories of freely-falling masses to diverge. We see this in the sky: distant galaxies are freely-falling but their trajectories are away from each other (and from us).

As far as we can tell though, the "source" of dark energy is the cosmological constant. Physical interpretations usually start by slicing spacetime into spaces aligned along the cosmological time (the scale factor). In successive spatial slices ordinary matter, radiation, dark matter, and so forth all get sparser towards the future. We treat these as a sort of fluid or gas that dilutes away with the expansion of the universe, therefore the density of each fluid at a typical point differs from spatial slice to spatial slice (it's lower in the future). The cosmological constant is constant in every spatial slice. So if we were to turn it into one of these fluids, it would not dilute or thin out over time: its density at a typical point is always the same. Representing a geometrical feature (the cosmological constant) as a space-filling fluid with certain properties makes it easier to study what happens if the cosmological constant isn't constant . (Does it fluctuate? Does it get weaker or stronger over time or in the presence of overdensities of matter?)

Cosmic inflation introduces another of these fluids that like dark energy serves to separate rather than draw together the others. It's very very strong in the early part of the universe (the inflationary epoch), but disappears very early too. In some flavours of inflation, the "inflaton" field decays into standard-model matter; in others it just decays into weaker and weaker versions of itself and by the time there are electrons, positrons and photons it's basically so weak that it's undetectable.

The inflationary epoch somewhat matches your intuition that a big source of energy pushed space apart. The most important difference (at this "explain like I'm..." level) as far as I can tell is that there was no point in space that someone in the early universe could point to as the centre or source of inflation. A gravitating object has a centre of mass, and you can point to and away from that object, i.e. there is an up and down with respect to it, because it doesn't surround you like a shell. The inflaton field was strong everywhere, there was nowhere in space "outside" it.

Here is a reasonably accessible "outreach" article on cosmic inflation: https://www.ctc.cam.ac.uk/outreach/origins/inflation_zero.ph...

Wald, §12.1, footnote 1.

Alternatively, and thinking purely classically, if we do t -> -t, what happens to a perfect absorber, which takes in anything and reflects nothing impinging on it? It should spit out arbitrary things and reflect everything impinging on it. (Here I'm thinking of the Poynting vector for plane waves with their origin below the photon sphere and moving outwards vs just above the antihorizon and moving inwards -- the latter can't enter the WH).

(Maybe easier to think about if the BH absorption isn't total, like if we spin the black hole and have the plane waves (or their polarization) move against the rotation, and the WH is just time reversed -- the WH emits a bit of radiation which joins more outside the antihorizon, and the combination flies off to infinity, and not thinking too hard about the interior metric; although Wald deals with much of this in the text around eqn (12.4.18)).

These are good questions. I'll get to the core of them after a one-paragraph rant about the aggregator linked at the top, and three paragraphs about how this bit of "science communication" (s̶c̶a̶r̶e̶ sarcasm quotes) means no answers for you about this particular visualization. I did end up peppering in a couple relevant bits of information in them though. In case it's not clear, the ordering of paragraphs below is not the order in which they were written.

Preliminarily: phys.org is hot garbage. It mostly reproduces institutions' (universities, NASA) press releases with its own ads. Rarely there is original content of dubious quality. This is not the latter, it's just a NASA-written blurb. Fortunately the same content is at the original source https://science.nasa.gov/supermassive-black-holes/new-nasa-b... -- absent that I probably wouldn't have started an answer.

Unfortunately the NASA link and its link to youtube give too little information to say anything reliable about the numerical relativity (NR) "codes" (s̶c̶a̶r̶e̶ jargon quotes) for this particular visualization. Yes, it's pretty and cool; yes it will excite relativists as well as laypersons; however, how about tossing the former a little drop of technical information? The supercomputer used and how much time was spent on it is not really useful to know.

I can only guess that the visualizer, Jeremy Schnittman, would want to generate data using the tools with which he's most familiar. Digging around in his publication history <https://scholar.google.com/citations?user=MiUTIQwAAAAJ> I see that he uses lots of Monte Carlo methods, often averaging over many very slightly different simulations (which might individually be wrong). I can see that for his black hole related work (mostly studying X-rays flying about just outside black holes, but also other phenomena close to but outside the horizon, or a little before the most strongly relativistic parts of black hole mergers) he prefers his own (Monte Carlo) tool Pandurata, which is described in Schnittman & Krolik 2013 <https://iopscience.iop.org/article/10.1088/0004-637X/777/1/1...>.

It is not at all obvious to me, especially given the scant information provided by NASA publicity, how he would safely apply these sorts of toolsets to the interior black hole metric. We aren't even told what the metric is, really; I assume Kerr with modest angular momentum, given his previous publications focus on astrophysically-reasonable Kerr black holes. There's another hint in what in the video looks like dimming at the receding limb (on the right) of the accretion disc. But this visualization could also be just Schwarzschild. Who knows? I look forward to his own professional writeup!

[Other NR tools are available, e.g. <https://nrpyplus.net/> and <https://grchrombo.org/movies/>]

Consequently I'll focus in on this part of your comment:

> these kinds of scales [or] galaxy simulations [...]

This is in the realm of numerical relativity and computational astrophysics respectively. There is an overlap.

Although I had in mind a couple resources about your questions, they're mostly textbooks which aren't freely available. So I first visited Sebastiano Bernuzzi's always useful syllabus http://sbernuzzi.gitpages.tpi.uni-jena.de/nr/ (nr is for Numerical Relativity, solving Einstein's equations with computers) and picked out two useful freely-available resources to start with. They are both called "lecture notes" but are really mini textbooks. They both have excellent bibliographies.

Choptuik's 2006 "Numerical Analysis for Numerical Relativists" (PDF) http://laplace.physics.ubc.ca/People/matt/Teaching/06Mexico/... is awesome. It focuses on finite difference techniques, which dominate in numerical relativity, particularly where black holes are concerned.

Like many others, Bernuzzi's 2021 3+1 Numerical Relativity <http://sbernuzzi.gitpages.tpi.uni-jena.de/nr/notes/2021/main...> points to it in section 2.4, where you will find references to other and newer treatments of various numerical relativity methods. Other techniques get used too, finite-element, for example. For galaxy stuff, you would want a resource on e.g. smoothed particle hydrodynamics or particle-particle/particle-mesh-Ewald.

ETA^2: wow, an actually useful physics SE q&a on that last bit (contrasting finite difference & finite element methods for black holes) from a little less than two years ago (direct link to imho good answer): <https://physics.stackexchange.com/a/725998>

ETA: this is more just a bookmark for me. Even though, like Chopotuik above, it's 17 years old, <https://www.cita.utoronto.ca/~pfeiffer/talks/07Apr_Jacksonvi...> is a really great slide deck.

ETA^3: Bernuzzi "Introduction to Numerical Relativity" @ IHÉS winter 2024 https://www.youtube.com/watch?v=RcdntEBrcuM is probably pretty good.

Yes, we can be certain. White holes can be considered in two ways: (1) a region of spacetime into which nothing can ever cross, with a surface that is a perfect reflector; or somewhat less commonly (2) a time-reversed black hole.

At scales of gigaparsecs, the universe appears to be both spatially homogeneous and isotropic, with matter denser at higher redshift. There is no way to generate this configuration of matter from a white hole. White holes are very much spatially anisotropic, that is you can point to where they are: left of you but not right of you, in front of you but not behind you, etc. The trajectories of the centres of momentum of galaxy clusters in every direction and at every redshift are diverging but not following an inertial radial. The really compelling accessible evidence against a white hole big bang is in the https://en.wikipedia.org/wiki/Lyman-alpha_forest from hydrogen clouds at different redshifts being backlit by bright background (and thus earlier in the universe) sources. This "stacking" is so hard to conceive for a white hole big bang that as far as I know, nobody has actually written down a reasonable explanation for it. More technically, (general relativity) metrics at those "cosmologically large" scales are so different from the metrics of white holes that we would already have noticed.

Additionally, a white hole big bang has to account for the chemistry of the earliest visible stars, whose spectral lines indicate essentially hydrogen with a tiny amount of helium and lithium. The standard cosmology's big bang nucleosynthesis's chemical abundances would have to be duplicated by a white hole big bang, and as far as I know nobody knows how to make that work. How does whatever is spit out of a white hole interior, or reflected off a white hole boundary, eventually turn into atomic hydrogen (with a smattering of heavier atoms up to 7 atomic mass units)? How does it account for the cosmic microwave background, which implies that in some region of the white hole big bang universe atoms practically everywhere were so hot as to be completely ionized?

Likewise, the interior metrics of black holes are very different from metrics which reasonably describe observations at gigaparsec scales. So if one takes a "wormhole" maximal extension of a black hole spacetime and throws enormous amounts matter into the black hole end, what emerges at the white hole end is nothing like a cosmology. Nor is what's inside. So a reasonable prediction of our galaxy's future is not exiting from a white hole (with us presently inside), and a reasonable prediction of our past is not that our galaxy was spit out of a white hole (with us presently outside).

As far as I know, nobody has done a convincing treatment of a non-eternal white hole in General Relativity. We've had theoretical models for forming black holes (i.e., there is a past of the black hole where there is no black hole yet, so it's non-eternal) since the 1930s (<https://en.wikipedia.org/wiki/Oppenheimer%E2%80%93Snyder_mod...>), and models for evaporating black holes since Hawking 1970, so it's quite striking there's nothing similar for white holes. There is ample astrophysical evidence supporting a range of models for non-eternal black holes and their horizons. There isn't anything seen by our telescopes that looks like it might be a white hole horizon.

The accelerated expansion of the universe, discovered in 1998, kills off a bunch of vaguely related ideas, like we are in a tiny tiny fraction of a thin shell (thin as in small compared to the shell's diameter) of matter that is expanding inertially from an initial impulse (an "explosion", figuratively) acting on a dense phase of matter. By "tiny tiny" here we're talking about our visible universe occupying less than 10^-23 of the shell's thickness. This is from a family of ideas tossed around a bit before Alan Guth published his 1997 book <https://en.wikipedia.org/wiki/The_Inflationary_Universe>. One could imagine a reflector onto which the shell fell, and that reflector could resemble a white hole; you can get a cyclic cosmology by having the entire shell eventually reconverge on the central reflector. However, we now see the expansion of our universe is speeding up rather than slowing down, so this doesn't work.

Finally, we're learning a lot more about the gravitational wave background of our universe. It is reasonable to bet that studies of the polarization of the cosmic microwave background (e.g. <https://lweb.cfa.harvard.edu/~cbischoff/bicepkeck/>) will find evidence of gravitational waves at scales large enough and uniform enough to rule out any sort of hole-like boundary (i.e., a one-way-crossing-only surface which has a spatial direction as well as being in the past) during the inflationary epoch. And we are probably already at the ruling-out point with baryon acoustic oscillation galaxy filament https://svs.gsfc.nasa.gov/13768 evidence.

tl;dr : enough incoming light will be scattered out of the central region around the focal point that you can't turn a "vacuum" central region into a spherically symmetric non-rotating black hole with masses less than tens of thousands of suns, when you start with a spherically symmetric shell of light.

Choice quote, after equation (9): "The intensity required to form a laboratory-scale kugelblitz (R ~< 1m) would be of approximately 10^83 W/m^2, more than 50 orders of magnitude above the state-of-the-art laser pulse intensities, which reach 10^27 W/m^2. For astrophysical sources, the intensity required is still many orders of magnitude above he highest-intensity sources in the universe, including quasars and supernovae [...] total power input must [be much more than] the bolometric luminosity of the brightest quasars [...] for any kugelblitz radius above the Planck length."

The authors conclude: "a localised electron can be more accurately represented as a condensate – an extended state comprising of photons and electrons. This model deviates from the traditional point-like conception of an electron, introducing a framework where a quantum electron exhibits non-point-like characteristics when localised".

Which why not, given a modern understanding of protons?

See also https://en.wikipedia.org/wiki/Electromagnetic_mass

Thanks, that's always useful.

§3 Discussion: "The estimated mass is also too large for one neutron stars or two neutron stars in a close orbit, so we are left with the possibility of: 1) a single BH; 2) an inner binary containing two BHs; or 3) a BH and another compact object. Although the single BH is the simplest explanation, the hypothesis of an inner binary of two BHs cannot be excluded [...] radial-velocity [...] perturbations are too small to be detected in the Gaia RVS [radial-velocity] data[.] For the purposes of the subsequent discussion we have adopted the single BH hypothesis as the most likely explanation."

Someone with more patience (or more troll-energy) than I have right now might try to introduce this into the handful of threads here containing various complaints that (clearly assuming a single BH), "size" is being punned as mass in the newspaper article linked at the top. If, for example, the ~33 M_sun ("mass of the sun") mass is evenly divided between two central BHs with the giant branch star companion orbiting them (cf. Alpha Centauri AB + wide companion Alpha Centauri C and similar triples), what's the most reasonable understanding of "size"? Or what if the dark component has a mass-ratio of ~ 30:2 split between a BH and a satellite NS? Total mass remains ~33 M_sun, how has "size" changed?

(Answer: "it hasn't". Generally I agree with the comments that read "size" as meaning mass and disagree that it should mean the Schwarzschild radius, and not just because the dark component might not be very Schwarzschild-like at all. Perhaps someone might do an ELI5 of dimensional analysis g = T^-2 L -> M = T^-2 L^3 or Gauss's law for gravity. (Serious ambition would be ELI12 of the argument around the "scale separation" towards the end of the excellent <https://physicscourses.colorado.edu/phys2210/phys2210_fa20/l...>, where we'd distinguish the scale of a possible inner-binary from the scale of the giant star's orbit around it.))

> Nothing to do with the missing baryons problem.

WHIM. Nicastro et al (2018) https://www.nature.com/articles/s41586-018-0204-1 (you can get a PDF at </https://arts.units.it/bitstream/11368/2935866/4/2935866_s415...> or the preprint at <https://arxiv.org/abs/1806.08395> and there is a nice summary at <https://www.esa.int/Science_Exploration/Space_Science/XMM-Ne...> ).

> If you had a large enough cloud of intergalactic matter it would form an event horizon

I assume you mean that you get gravitational collapse and some form of ~ 2GM black hole horizon (pfdietz's "any material (of any density) can be made a black hole if there is enough of it"). Trivially you can get an event horizon by making the cloud a Rindler observer, or even more trivially by making it an Eulerian observer in de Sitter space. So let's think about what makes a diffuse cloud collapse in a universe like ours at a comparable scale factor.

At the GR level (e.g. matter dominated era OS or LTB like versions of Einstein-de Sitter or similar dark energy dominated era approaches) the problem you encounter is that you end up having to exchange matter between the collapsing "large enough" cloud and the expanding radiation (and other FLRW fluid) filled cosmological region in which it is immersed, and you have to keep a check on the false intuition that leaking stress-energy from the nonvacuum cosmological region into the vacuum in the collapsing cloud -> black hole region is OK to stabilize pressure, because that's not what we see.

We could alternatively look at it through the lens of Jeans instability. To get collapse you need undamped perturbations with oscillation length longer than the Jeans length, which increases in proportion to temperature and decreases in proportion to mass density and mean molecular mass. And then you have to avoid fragmentation. Which takes us to...

> direct collapse [SMBHs]

Sure, in z > 15, the metal-poor radiation dominated era or even earlier, it's plausible (but see below). You need to avoid the formation of molecules or the gas will radiatively cool much faster than it will contract, fragment your cloud and drive cluster star formation. Greedy metals (carbon, oxygen) will kill direct collapse dead. More relevantly to a hypothetical cold intergalactic medium, you need a lot of UV (Lyman, Werner) photons to bust up molecular hydrogen. (But as far as we can tell from e.g. <https://savechandra.org/> the actual intergalactic medium is not cold: <https://astronomy.swin.edu.au/cosmos/I/Intergalactic+Medium> and so the Jeans length is lonnnnnnng).

However, if we have a sufficiently large and cold gas cloud in the dark energy dominated era, with quasars dim and distant, how do we keep it from diluting away with expansion or alternatively fragmenting into overdense and underdense regions? I think the inevitable answer is you need higher mass density and not "any density", which was my point.

Now I'll stray from my island of comfort. I don't do galaxy dynamics or formation and evolution, and I think black holes are mostly pretty boring, so the next two paragraphs and the final one are out of my areas of focus, and there are likely to be gaps and errors. For me, this stuff is all the wrong age, the wrong spatial volume, and/or the wrong energy.

> SMBHs ... from direct collapse [again]

DCBHs (if they exist and if they are the missing step in a hierarchical building of SMBHs by z ~ 7; here supermassive means 10^5 M_sun rather than some of the monsters in the local universe) are due to a direct GR instability in supermassive pop III stars, and have masses around 10^5 M_sun. DCBHs are metallicity limited (thermonuclear kablams), with critical metallicity increasing enormously near and above 10^6 M_sun or so.

If we take the lower end of SMBHs at ~ 10^5 M_sun, then you're right that there are theories of how they may have formed from direct collapse of large but diffuse clouds. A number centre on Priyamvada Natarajan. The introduction of Goulding, Natarajan et al. 2023 <https://arxiv.org/abs/2308.02750> on the weirdo UHZ1 (very dust obscured luminosities from <https://savechandra.org/> X-ray and NIRSpec has a very early z ~ 10 SMBH that seems very unusually massive compared to the host galaxy) lists a few: "Theorists have therefore explored alternate seed formation models, with heavier seed BH mass functions (∼ 10^4 M⊙) that could form from the direct collapse of gas in the high redshift Universe (Lodato & Natarajan 2006, 2007; Volonteri et al. 2008; Inayoshi et al. 2022, see for instance)." Natarajan in a nearly-simultaneous paper on UHZ1 <https://arxiv.org/abs/2308.02654> accepts that a 10^4 M_sun heavy seed is sufficient to explain UHZ1's SMBH:host galaxy mass ratio, and of course 10^4 M_sun is within the range for pop III DCBHs.

Context for next paragraph: "larger than the size of our galaxy ... direct collapse of large ... clouds". I apologize if you did not mean to link your second and third paragraphs that way.

I don't know of many ideas that propose direct collapse into SMBHs much above that lower limit. Directly collapsing a dying supergiant star is hard enough, and much of the work is done in the earlier life of the star. Directly collapsing a 10^12 M_sun or heavier cloud without going through star formation (which would fragment and blow apart the cloud through radiative cooling and reheating) is a pretty wild idea!

>> any object can become a black hole if it is made dense enough

[big 'if'!]

> any material (of any density) can be made a black hole if there is enough of it

There is an awful lot of intergalactic medium out there. It's of "any density" (albeit very low). How come it's not a black hole? Isn't there "enough of it"? (cf. the "missing baryons problem").

There is an awful lot of atomic and molecular hydrogen gas in the Milky Way and practically every other galaxy. In our galaxy it totally dwarfs all the matter in our central black hole, the stellar black holes, and in all the luminous stars combined. Seems like "enough of it". It's of "any density". How come it's not a black hole?

And so forth.

> (actually, one should properly talk about the circumference)

Why? Also, since we're being properly, what's the circumference of a spinning black hole and how does it evolve with the spin parameter?

Extra credit: assume that you mean the mean density of the interior of M87*, how are you arriving at its volume? (You might cast your eyes over Bengtsson & Jakobsson's extension of work on this question by Christodoulou & Rovelli at respectively https://arxiv.org/abs/1502.01907 and https://arxiv.org/abs/1411.2854 -- when you calculate the volumes in a relativistic spirit, the interiors are very large, far too large to support your (commonly used) throwaway line about dense-as-air/less-dense-than-water). Alternatively, what do you think the BH interior modal densities are?

("In their paper CR [Christodolou & Rovelli] estimate that the black hole at the centre of the Milky Way — whose area radius they assume to be not much larger than the distance to the Moon — now contains enough space to fit a million solar systems. A decent estimate for its spin appears to be a/m ≈ 0.9 [5]. It follows that CR overestimate the volume, but only by a factor of 10 or somewhat less". And from CR: "flat space intuition does not apply to the curved geometry inside the hole [...] and the interior volume keeps growing with time").

I of course expect this comment to be thrown into a deep (gravitational) well, actually.

> If you (the neutron star) gain mass near the gravitational field, it pulls you in closer.

This conflicts with the Strong Equivalence Principle (SEP) in its universality of free fall form, or more colloquially a rule that the trajectory of a self-gravitating object depends only on its initial position and velocity and not on its internal composition (including the evolution of its mass).

There is a good test of the SEP in a system involving the millisecond pulsar https://en.wikipedia.org/wiki/PSR_J0337%2B1715 which is in a hard binary with a white dwarf; a second white dwarf orbits the inner binary. Here is a trace of the orbits https://www.youtube.com/watch?v=oDgfqq_W_uM -- I recommend reading the video description.

Reference 2 (Archibald et al.) at the wikipedia page is an excellent paper.

There are a couple of good astrobites aimed at (advanced, or possibly final-year) astrophysics undergrads at https://astrobites.org/2014/01/14/timing-is-everything-a-pul... (2014) and https://astrobites.org/2019/03/25/testing-einsteins-equivale... (2019)

You're right that the flow of mass in a complex system might be relevant to the merging binary, but in general a stellar black hole's circumstellar accretion structure isn't going to do much to a close-in neutron star except create a lot of (relatively small) nuclear explosions on the latter's surface. There just isn't going to enough material in the accretion structure in comparison to the bigger bodies, which will have masses greater than our sun.

Accretion structures are more relevant for softer (that is more widely separated) binaries, which are a long time before final merger. Circumstellar accretion discs can be in association with a circumbinary disc (CBD; outside the binary), with a flow of matter between them (one would expect the CBD to be the origin of the circumstellar discs, but jet outflows make that expectation complicated). CBDs tend to circularize wide binary orbits, for example. They also provide mechanisms to harden binaries that might seem so soft that a merger could be avoided.

You're right that some neutron stars may have very strong magnetic fields that may affect its accretion disc or the (randomly aligned) accretion disc of its black hole binary partner, but again the flows of mass near the binary must be much less than the masses of the relativistic stars (the NS and the BH), as the each of the stars are very very strongly bound self-gravitation.

Your idea bout mass flow is interesting -- it takes my mind to how much of the accretion disc might be blown into ~polar jets, and how complicated the alignment of spin axes are to the orbital plane can be late in the merger. The accretion structures are I guess likely to be blown into a CBD (or out of the system entirely) well before final merger. Either way, the masses involved likely won't change the inspiral significantly.

If the NS shreds (as opposed to being swallowed whole, which is the more likely outcome, and the apparent outcome in this detection) the additional matter in an accretion structure (including any accretion material blown out of the system via jetting) could be relevant in the r-process and s-process heavy element formation processes. Realistically though that's the sort of question more relevant to binary neutron star mergers.

(As a sort of self-bookmarking and because it's probably interesting to other readers here, Maria Massi's 2020 "Accretion" teaching slides at https://www3.mpifr-bonn.mpg.de/staff/mmassi/lezione2WEdd.pdf are awesome, and takes one to some work on x-ray binary circumstellar discs and even circumbinary accretion. More recent review on the latter <https://arxiv.org/abs/2211.00028>, and figure 1 is probably helpful for a couple of my paragraphs above).

Good question! I'll try an answer and hope it's a good balance between accuracy and what I guess is your (and other readers') knowledge of astrophysics.

[tl;dr: a neutron star (NS) and black hole (BH) in a close binary are practically guaranteed to "crash" into each other eventually. There seem to be lots of those binaries. Neutron star - black hole mergers (NSBH) from other possible arrangements (wider binaries, isolated individual NSes and BHs) will be vanishingly rare in "the local universe".]

There are two principal branches in an answer to your question.

First branch: there are probably lots of individual isolated neutron stars and black holes within galaxies, and those are unlikely to form binaries with each other, or get anywhere close to each other (except maybe possibly in the very centre of galaxies, or in the very far future). I won't spend time on this branch in this comment, even though this is the branch which interests me personally (at a theoretical rather than astrophysical level). In reality, isolated stars and star systems within galaxies just do not seem to collide with one another and isolated neutron stars and (stellar mass) black holes are no different.

Independent isolated stars may form binaries under rare circumstances such as galaxy-galaxy mergers or in radiating globular clusters within galaxies. The same goes for isolated neutron stars or stellar mass black holes. In those cases they can fall into the next paragraph.

Second branch: there are probably lots of neutron stars and black holes already in close orbit with one another, and those orbits will over long times decay (because such binaries radiate nontrivial gravitational waves) leading to a "crash". Tight orbits involving two relativistic bodies (white dwarf (WD), neutron stars, black holes) are unstable and practically always lead to a merger; there are a number of ways a looser/softer binary of such bodies can become a tighter/harder one, including during the transition of a dying star into a WD, NS, or BH.

Multi-star systems are commonplace[1] and likely mostly born as multi-star systems (e.g. within a nebula originating in the explosive demise of earlier more massive stars), rather than starting as individual stars that just get close enough to start orbiting each other.

One could compare this to how Jupiter and the sun most likely formed from the same part of a giant molecular cloud (GMC), rather than a fully-formed Jupiter being captured later by the sun. Likewise, the Alpha Centauri system probably formed as triple-star system within a different part of the same GMC, rather than the inner AB binary capturing Proxima Centauri (C) or each other. (Triple star systems with an outer member orbiting an inner binary are pretty common, even very close to us in the galaxy).

We'd expect therefore for a proportion of aging multi-star systems to evolve into binaries of "dead stars" including inner neutron star - black hole binaries. Those inner binaries will practically inevitably decay resulting in a neutron star - black hole merger (NSBH) producing a signal in-principle detectable by gravitational wave detectors like KAGRA, Virgo, and LIGO. (The outer member of a triple or surrounding gas, dust, asteroids, and comets can help tighten the inner binary.)

Gravitational wave detectors like LIGO are range-limited, with the current range about 200 megaparsecs (about 600 million light years), which is on cosmological scales quite local. We've counted about a quarter of a million galaxies[2] in that range. By comparison there are hundreds of billions of galaxies in our sky.

A fraction of neutron stars are pulsars. Because of the practicalities of radiotelescopes, at present we can only really find pulsars nearby within our galaxy (dust obscures a lot of the galaxy at the relevant radio frequencies, and there is only one extragalactic pulsar known, and it's in the neighbouring Large Magellanic Cloud). However, we've found several thousand pulsars (see final paragraph below). A sizable fraction are in multi-star systems, which we know from tracking radial acceleration in several ways, and because among these are a handful of eclipsing binaries. There are known pulsar-pulsar pairs (famously, <https://en.wikipedia.org/wiki/Hulse%E2%80%93Taylor_pulsar>) as well as more complicated systems which include white dwarfs and maybe black holes.

From gravitational wave observations, we can spot a NSBH even if we can't see either individual body (in radio or other parts of the electromagnetic spectrum) because of obscuration by dust and other foreground matter, or because the NS is not a pulsar and thus both objects are very faint in radio. We don't have a good census of dim neutron stars even in our part of the galaxy. However, there will be more dim neutron stars than radio-bright pulsars, and it is reasonable to guess that there will be more dim neutron stars in binary- and multi star systems with a black hole than there are radio-bright pulsars in such systems.

So looking at one galaxy (ours), we can guess that if we waited a few million years we would see a decaying hard neutron star/black hole binary eventually merge. So naively, we might think that if we waited a few years we'd see an NSBH merger from among about a quarter of a million galaxies. And at gravitational wave detectors we're seeing more NSBHs than that naive estimate. So perhaps pulsarNS-BH binaries are rare compared to nonpulsarNS-BH ones. Or perhaps there are lots of pulsarNS-BH binaries in the Milky Way hidden behind dust and sources of radio noise.

Finally, this interactive map of known pulsars https://ishivvers.github.io/maps/pulsars.html is so cool I've submitted it separately at https://news.ycombinator.com/item?id=39970373

[1] "Stellar Multiplicity" (arxiv version of published ARA&A paper), Duchene et al. 2013 https://arxiv.org/abs/1303.3028

"Multiple Star Systems" (multimedia outreach) https://science.nasa.gov/universe/stars/multiple-star-system...

(examples) https://en.wikipedia.org/wiki/Category:Triple_star_systems

(more examples, quadruples and beyond) https://en.wikipedia.org/wiki/Star_system#Quadruple

[2] section 5.3 of "Census of the Local Universe [..]", Cook et al. 2019 <https://ui.adsabs.harvard.edu/abs/2019ApJ...880....7C/abstra...>

If you prefer to read on arXiv, https://arxiv.org/abs/hep-ph/9908313v2

Abstract:

"The solar neutrino counting rate in a real time detector like Super--Kamiokanda, SNO, or Borexino is enhanced due to neutrino oscillations in the Moon during a partial or total solar eclipse. The enhancement is calculated as a function of the neutrino parameters in the case of three flavor mixing. This enhancement, if seen, can further help to determine the neutrino parameters."

tl;dr on this long comment: the article is about a 1960s mistake and how a paper demonstrates an improved model Earth that has non-uniform density can do better than the simplest fix. New Scientist gets an important bit of science wrong, surprise. And some links to even deeper (pardon the pun) studies of the relativistic effects of Earth's gravitation.

Well, even though this is resurrected from 2016 it seems to have captured my attention for a bit. :-) Before this HN posting I had not read the article nor the paper it discusses. (I had read all the other linked items below.)

The arxiv version of the paper <https://arxiv.org/abs/1604.05507> (Uggerhøj et al 2016) without saying so in words does post-Newtonian ("PN") corrections to Poisson's equation for Newtonian gravitation <https://en.wikipedia.org/wiki/Poisson%27s_equation#Newtonian...> (note the last equation in that section is the same as the paper's eqn (1)). The corrections enter with constant multiplications by c^2 and the reciprocal. Wikipedia is not helpful: <https://en.wikipedia.org/wiki/Post-Newtonian_expansion#Expan...> is only a paragraph long. Clifford Will's 2011 PN paper is an excellent overview, and the first two pages or so (of nine total) are reasonably accessible to undergrads and laypersons (arxiv version: <https://arxiv.org/abs/1102.5192> and from there you can get a link to the published PNAS version if you somehow prefer that interface). For laypersons Gerhard Schäfer's "Step by step from newton to Einstein" <https://www.einstein-online.info/en/spotlight/postnewton/> is very good.

There is nothing wrong with the authors (or Feynman) treating the relativistic age difference as a problem approximately solved using PN methods. (I'll justify that near the end of this comment). Probably that's what Feynman did, and of course Einstein essentially invented PN methods due to a lack of computers of any sort to help solve problems in the full theory of General Relativity. The Uggerhøj et al. 2016 paper itself somewhat too carefully restricts itself to expressions like "time dilation in relativity" and "relativistic aging", never outright deploying the words "General Relativity" or its exact synonyms, without explaining why. The abstract goes a bit too far with this, imho, "... a fairly complete solution to the relativity of 'aging' of an object due to differences in the gravitational potential" is strictly true -- although "fairly" does some heavy lifting -- and "differences in gravitational potential" is simply not from General Relativity and its curved spacetime, but rather from Poisson's equation for Newtonian gravity with corrections for the finite speed of the (Newtonian) force of gravity.

I think Uggerhøj et al could reasonably expect a reader to misunderstand their paper as an analysis using General Relativity, and indeed that's exactly what Jacob Aron (the author of the New Scientist article) did: "Physicists have calculated ... the effects of gravity as described by general relativity." No. They have not.

(Does this matter? Yes, the moment you introduce an observer moving faster than a few percent of c, you get can get bad results from expansions in orders of v^2/c^2. Does this matter for the purposes of using depth-dependent differences in isotope abundances as a notion of "age", which was the focus of Uggerhøj et al. and (according to them) Feynman? No, probably not. But if you had a Earth-observing neutrino satellite sensitive to beta decays at depths from the surface to the core, and that satellite were in low Earth orbit, you'd want a check on any PN methods relying on v being much less than c (again, see near the end of this comment) which might be used in analysing the observed beta decay spectrum. Not total sci-fi: for example Borexino <https://borex.lngs.infn.it/> picks up (anti-)neutrinos from the Earth, and smaller detectors of "geoneutrinos" is an interesting area of research).

The central message of Uggerhøj et al paper (which the New Scientist article gets acceptably right) is that sources are important in gravitational physics, and that a better description of the Earth's bulk composition gives more reliable results. That's true in the PN case (as discussed in the article) as well as well as what we'd want to do in General Relativity: set out the stress-energy tensor (a description of the matter and its non-gravitational interactions) and feeding that into the Einstein Field Equations to extract the metric tensor. Even today we can only attempt the latter numerically with supercomputers; there was no realistic path to such a solution in the 1960s.

But for most practical purposes (including GPS and other GNSS) we are fine with low-order PN corrections for the Earth's gravitational field (measured empirically using artificial satellites, lunar laser ranging, and other tools in geodesy and geodynamics) -- see for example the excellent Soffel & Frutos 2016 "On the usefulness of relativistic space-times for the description of the Earth's gravitational field", <https://link.springer.com/article/10.1007/s00190-016-0927-4> which (because Springer sucks) you should obtain via s c y h o b <https://sci-hub.se/https://link.springer.com/article/10.1007...>, which makes the case that "the first post-Newtonian approximation is completely sufficient for a description of the Earth's gravitational field and also for a description of satellite orbits" and "the use of a higher post-Newtonian or even exact metric [i.e., General Relativity] is not justified as long as a theory of relativistic systems is not available at [present day] level of accuracy."

Finally, anyone comfortable with gravitational theory is likely to enjoy Philipp et al. 2020 https://doi.org/10.1103/PhysRevD.101.064032 aka https://arxiv.org/abs/1912.10159 ("Comparing the Earth’s Newtonian geoid to its relativistic generalization is a very subtle problem, but of high interest")

Duplicate of https://news.ycombinator.com/item?id=39925930 (posted about 13 hours earlier)

The published paper linked at the top corresponds with https://arxiv.org/abs/2303.03545 if you prefer the arxiv interface.

This is a remarkable amount of work (some of it genuinely interesting) for an April Fool's joke!

That seems a bit excessively nitpicky. Neither you nor the comment you corrected somewhat is really wrong. I'm not sure you're much more right, though. Thomas-Fermi screening and the Coulomb crystal lattice of the outer crust isn't very plasma-like (and differs from the astrophysical plasma in the accretion disc). Perhaps it's better to say that it's a phase of matter unlike the "classical four", and more like one of the dozens and dozens of known condensed matter states. Chamel 2007 is pretty interesting on that front: <https://arxiv.org/abs/0709.3798>.

I would agree with you about the inner crust, and so would Chamel (and many others): "Unlike the situation in ordinary solids (ordinary meaning under terrestrial conditions), the electronic properties in neutron star crust are very simple. The matter density is so high that the Coulomb energy of the electrons is negligible compared to their kinetic energy" [which is essentially your point] "The electrons can thus be treated as a degenerate relativistic Fermi gas." Chamel 2008 is also excellent <https://link.springer.com/article/10.12942/lrr-2008-10>.

More recently Taverna et al 2022 <https://www.science.org/doi/10.1126/science.add0080> does X-ray polarization spectroscopy on candidate magnetar (Anomalous X-Ray Pulsar AXP) 4U 0142+61 <https://en.wikipedia.org/wiki/4U_0142%2B61> (follow links in [6] therein) to investigate the physical state of the crust, finding the best match is a solid and bare surface.

Finally, the phys.org article at the top corresponds with Russel et al 2024 <https://arxiv.org/abs/2403.18135> which as far as I can tell has practically nothing to do with this thread of discussion nor the paragraph in the phys.org article that motivated it. Perhaps the phys.org article writer confused accretion "hard state" (relatively low mass accretion rate, p. 3 of Russell et al. 2024) with a stiff (or hard) outer crust equation-of-state which compresses poorly compared to an EOS softened by neutronization (e.g. Haensel, P., Potekhin, A.Y., Yakovlev, D.G. (eds) (2007), chapter 3 <https://link.springer.com/chapter/10.1007/978-0-387-47301-7_...>).

The excellent overview and somewhat different approach to the NS EOS in Sumioshi et al 2022 is pretty neat too <https://arxiv.org/abs/2207.00033>.

They're trying; it's the subject of the second paper referenced at the end of the link above (direct link: <https://iopscience.iop.org/article/10.3847/2041-8213/ad2df1>, open access). It's a bit complicated but (for our galaxy's central SMBH, Sgr A), from simulations they have a confidence interval spanning a few tens of Gauss at significant radial distance to a few hundred Gauss near the event horizon, or an average somewhere below 30 Gauss. Early measurements of M87 (<https://iopscience.iop.org/article/10.3847/2041-8213/abe4de>) arrived at somewhere between one and thirty Gauss (on average) for that black hole.

By comparison, Earth's magnetic field is about 0.5 Gauss at the surface. So Sgr A's averaged magnetic field is strong compared to that. However...

The Earth's magnetic field strength increases with depth below the surface, reaching about 25 Gauss at the core, which is a lot less than near the horizon of Sgr A.

But sunspots are on the order of a thousand Gauss.

The strongest magnetic fields human technology has been able to generate is on the order of tens of millions of Gauss.

A magnetar's field strength is at least tens of billions of Gauss.

Our black hole has not been feeding recently (as in, for the past many thousands to millions of years dating from the view we have of it here and now), so doesn't have much matter around it to drive the field strength higher. M87* is not feeding much either. The best working model for magnetars describes an early non-equilibrum state for the magnetar in which at intermediate depth a complicated nuclear fluid acts as a proton-dominated superconductor. Flows within that fluid act as a dynamo (well, really a magnetohydrodynamic (MHD) generator) for the magnetic field. A significant accretion structure around a black hole can also act as as an MHD generator. Weakly feeding black holes lack such a structure.

No, it's not just time-reversal; it's charge, parity and time reversal. You can't just time-reverse an electron neutrino and obtain an electron anti-neutrino, because the parity will be wrong, and so will the weak isospin charge and lepton number ("lepton charge").

https://en.wikipedia.org/wiki/CPT_symmetry

Worse, the symmetries of the Standard Model are pretty complicated, especially when one goes from the local Lorentz or Poincaré symmetries x SU(3) x SU(2) x U(1) to the global continuous symmetries that capture https://en.wikipedia.org/wiki/Custodial_symmetry, (particlularly QCD) flavour symmetry, and scale symmetry. There are some further long-range approximate symmetries too, and those get worse with spacetime curvature. These all may have to be accounted for if one is time-reversing a region of the spacetime-filling fields of the Standard Model.

> So where did all our antimatter go?

Good question. Nobody can really tell you right now. Maybe there are galaxy clusters totally dominated by antimatter, maybe the antimatter is in a different Hubble volume, maybe it all annihilated into the cosmic microwave background and other ultra-low-energy relic fields (e.g. the cosmic (anti-)neutrino background) we haven't detected or discovered yet, maybe into primordial black holes, maybe in an extension of the Standard model to extremely high energies there isn't a matter-antimatter balance in the first place. One can write down an enormous number of different theories, and relax knowing that there is presently no evidence to favour or disfavour it, provided it's compatible with the experimental and astrophysical evidence we have today.

(I do like the idea, building on an idea arising from Wheeler's one-electron universe, that anti-electrons (in this case more than one) are screened within pion condensates ("maybe they're hiding in neutrons", vaguely), because that makes the symmetries even crazier, and particle physicists deserve that).

[Below, keeping your choice of metric signature (+,-,-,-)]

> t^2 - x^2 - y^2 - z^2

Off by a constant factor (c).

> distance = [above]

distance^2.

This is still not quite right since we're interested in how coordinate changes affect the spacetime interval. So take distance -> S, the spacetime interval instead of the Euclidean distance, and then sprinkle in the deltas: dS^2 = c dt^2 - dx^2 - dy^2 - dz^2. That is the Minkowski metric (the flat metric of special relativity) in Minkowski coordinates.

The right hand side can be positive (for a timelike spacetime interval), negative (for a spacelike spacetime interval), or zero (for a null spacetime interval). Massless particles, when not accelerated, travel on null spacetime intervals, as do other solutions of massless wave equations. Light is rarely accelerated. However a null interval does not mean no distance, it only means that there is an exact balance between the spacelike portion of the spacetime interval and the timelike portion of the spacetime interval. An object moving against the t and x coordinates at speed "c" will (choosing units for clarity) tick off one second along the t-axis for every light-second it travels along the x-axis. A timelike trajectory ticks off more than one second per light-second along the x-axis; and a spacelike trajectory ticks off fewer seconds per light-second along the x-axis.

So, with light always in inertial motion, and always moving at "c", the spacetime interval for an element of light (classical or quantum) will always be zero. That does not imply in any way that the element of light does not travel at all. Also it does not imply that if we split the spacetime interval into timelike and spacelike components, that we find that the photon experiences "no time".

The confusion arises frequently because the usual way one splits a timelike spacetime interval (e.g. for a massive particle) into its timelike and spacelike components is to use the proper time interval (and that leaves us with proper lengths). Proper time is a specific affine time which can be caluclated for non-null spacetime intervals, but not for null spacetime intervals. We can use a different affine time for those instead (leaving us with affine lengths that are not "proper lengths"). But even so there are changes in coordinates (e.g. (t=0,x=0)->(t=10,x=10); the photon is ten seconds older and ten light-seconds further away along x).

[Experts who already know about invariance under coordinate transformations etc. should also know not to pick too hard at that last sentence. The point is that if we do c \def = 1, then 1dt^2 - dx^2 = 0 for arbitrary photon displacements along x and this is true at least up to rescaling.]

Curvature isn't necessary here; all we need is time-orientability, so we can even be more general than a Lorentzian manifold. We can achieve time-orientability by comparing how strictly we must constrain the degrees of freedom of, for example, an adiabatically expanding or contracting cloud of gas of non-interacting test particles below some critical mass-density such that expansion will carry on forever, rather than there being some eventual recontraction. This is perfectly doable in flat spacetime. It's essentially just a problem in statistical mechanics, as we can arrange time-orientability this way without having anything to do with relativity.

We don't really need time-orientability in relativity; it is perfectly reasonable to have solutions to the field equations which are static or stable periodic (and thus there is no clear past/future). Conversely, more generally we can get time-orientability in a wide variety of dimensions other than 3+1.

Relativity just tells us that where there is some global time-orientable feature, every observer will agree what's the past and what's the future of that feature. However, complex observers may have some internal degrees of freedom providing a local notion of time-orientability which could be unaligned with the global feature (and other observers' local features).

I don't see how any of this can relate to "consciousness" though. Also, our universe really doesn't admit backwards time travellers as far as we can tell, so whether and how the wider universe "corrects" observers who have different past/future orientations is really really really academic from a physics perspective. Sean Carroll's blog had a lot about that a decade or more ago, which you can probably dig out of preposterousuniverse.com or wherever.

ETA: this gathers up the bluesky thread readably https://skyview.social/?url=https%3A%2F%2Fbsky.app%2Fprofile... although you'll probably prefer "unroll" over "tree" (but "tree" seems to capture everything including a handful of replies).

Cross-posted to x/twitter: <https://twitter.com/duetosymmetry/status/1769913120099545488>

(ETA: there are 38 (thirty eight) entries in the thread. Logged in on x/twitter I see them all, but bsky (logged in and not) sometimes doesn't show them all in one scroll-through. :/ )

tl;dr (it's a very technical explainer thread)

[preliminary] this is physics, it is important to match GW (and optical) detections of mergers, not to model "spherical cows"

[a] post-Newtonian (PN) methods are cheap to calculate for black hole binaries when they are far apart (and other methods are good for extreme mass ratios) but in the last moments before merger we need numerical relativity (NR). NR is expensive even on supercomputers.

[b] PN and NR are different enough frameworks that knitting together the early inspiral PN and the late pre-merger NR requires some overlap and iteration.

[c] results from a couple dozen simulations give interesting technical insights

[d] orbital eccentricity (and ellipticity) make everything harder, especially for PN, because the plane of the orbit and the orientation of the black hole spins against the orbital plane all precess (and differently from each other)

Finally, if you can't see the thread on either platform, the prerpint is at https://arxiv.org/abs/2403.10278

(I did double-check and can read the bsky thread via the Tor browser (obvs. not logged in). x/twitter is ... uncooperative when not logged in. Finally, mastodon threading is ... confusing.)

You don't quite RC, because of the interstellar medium (and sometimes the circumgalactic medium). In a galaxy-galaxy collision, individual stars are almost collisionless, depending on the stellar density of the galaxies. However, if there's even a small fraction of the normal amount of gas in both galaxies, the interaction will be very X-Ray bright from gas friction. The behaviour of gas tends to dominate many if not most galaxy-galaxy collisions.

Good opportunity to plug https://savechandra.org/why/

NGC 2207 https://www.chandra.harvard.edu/photo/2014/ngc2207/ ("Colliding galaxies like this pair are well known to contain intense star formation. Shock waves — like the sonic booms from supersonic aircraft — form during the collision, leading to the collapse of clouds of gas and the formation of star clusters")

NGC 1232 https://chandra.harvard.edu/photo/2013/ngc1232/ (the text below the image is excellent).

Stephan's Quintet https://chandra.harvard.edu/photo/2009/stephq/ (be sure to use the "View Wavelengths" buttons right below the image, and mouse over the image for annotations)

There are lots of other examples. While brief <https://en.wikipedia.org/wiki/Interacting_galaxy#Galaxy_coll...> is decent, and can take you to the longer https://en.wikipedia.org/wiki/Galaxy_merger, which is pretty encyclopedic on that branch of galaxy-interaction outcomes.

Spongebob pretty clearly doesn't account for gas. The initial velocities are also not really comparable to a galaxy-galaxy interaction. And of course it's in two spatial dimensions, so fewer ways that any pair of particles might avoid each other than in our three.

And to answer the grandparent comment, the gravitational interaction of particle-particle close calls in Spongebob are suppressed, so no collisions. Gravitation is the only force modelled, so no clumping. I arrived at that from scattered Q&A comments in the twitter thread, but also it's pretty clear from eyeballing.

> Hawking radiation is due to process outside the black hole.

Hm, yes, the Hawking quanta originate outside the event horizon, and not very nearby outside either (Giddings 2015 <https://arxiv.org/abs/1511.08221>, Unruh "Dumb Holes" 2007 <http://pos.sissa.it/cgi-bin/reader/conf.cgi?confid=43>).

However it's best to think of "the black hole" as the entire spacetime (in Hawking's 1974 treatment and similar; or alternatively out to somewhere in the asymptotic flatness), in which there are two regions without a horizon, one to the past of the event horizon formation, and one to the future of final evaporation.

What goes into the horizon doesn't stay in, therefore what happens inside is part of the picture (and has been speculated about for fifty years! Fifty!)

There is a relationship in that both the "Spongebob cluster" and a black hole has negative heat capacity. The math is already there in the virial theorem. See <https://en.wikipedia.org/wiki/Heat_capacity#Negative_heat_ca...>. Detailed treatments of the non-relativistic case you can find in an undergrad astronomy textbook; the relativsitic singleton case ehhhhh I don't think you're ready for it but Wald's General Relativity §12.5 & §§14.3-14.4 would be a good choice (and he shows you the math, which has been known for several decades), and for relativistic orbits I think you need to go beyond textbooks (although you probably could start with numerical relativity textbooks, like Baumgarte & Shapiro or Alcubierre, although I don't have either handy to double-check where they go with thermodynamics. Oh and the paper I linked in a sibling comment has a good and relevant bibliography. <https://academic.oup.com/mnras/article/516/3/3266/6668807>).

I like your comment, it provoked some catch-up reading, so forgive me pecking a bit at what you wrote.

The visualization is pretty limited, and was probably just a fun way for the astrophys student to use his choice of tools. (Which we should encourage! His work is great!)

I am also not the only person to think the visualization would be useful when teaching early astro or astrophys undergrads. For example, <https://twitter.com/BenShappee/status/1769066245339402612>. (BTW, Shappee was in ASAS-SN from the start. ASAS-SN is awesome, I promote them whenever I can squeeze them in: <https://www.astronomy.ohio-state.edu/asassn/index.shtml>).

Digging deeply into the consequences of this example of obviously physically improbable initial conditions could be somewhere between entertaining and enlightening, but would quickly go over the head of early astro students first encountering the virial theorem and negative heat capacity. "Getting the physics right" would be a significant research project. You'd also generally have to do without animations, unless you are very patient and have a big compute time budget (see the acknowledgments section of the MNRAS paper below, and my final paragraph).

Motivated by the previous paragraph's themes I found a recent (2022) MNRAS open access paper which among other things has a good overview of the (recent) state of the art in modelling star clusters, some good teaching material in section 2, and in section 3 we see their software packages. I'd suggest you begin with the summary in section 6.1.

https://academic.oup.com/mnras/article/516/3/3266/6668807

In principle simulating the Spongebob cluster could produce information in the top two graphs of figure 7, and a 2d version of one or two of the graphs in figure 6. The additional information in those figures is certainly interesting, but nowhere near as pretty as the Spongebob animation. And I'm not sure what extracting similar figures for the Spongebob simulation would be useful for.

Conversely, the Spongebob simulation could not generate figure 9, and that figure is especially interesting to me (q.v. §4.2 & final sentence in §3.2).

And finally, "The movies of the full simulations, from which Fig. 6 was produced, will be made available upon reasonable request as well and will be uploaded publicly in the future". Not sure the upload ever happened, although I didn't really search much (e.g. it's not linked at the arxiv <https://arxiv.org/abs/2205.04470> or in DDG media searches on title or a few of the authors).

Good question. Without seeing the code that produced this, I'm stuck making some educated guesses.

The "splitting" effect is forced by the enormous computational expense of the numerical relativity calculations.

Instead of thinking of the initial yellow pulse as a plane wave, think of the animation as tracing-out the evolution of a number of representative initial positions in that plane wave. We don't see the full density of the many-many-many particle pulse in any frame. (We're also only seeing two spatial dimensions). We just see pixels lit depending on where the initial positions have led to.

We don't really see advancing "beams" as such, it's just that pixels are left lit even after they spatial positions they represent have emptied. The dimming of previously-lit pixels is artistic license.

The youtube video also doesn't show us the light's change in energy-momentum ("frequency", equivalently), although the twitter version in my other comment (or here: <https://twitter.com/PeRossello/status/1756697785083023812>) does, with the caveat in the second tweet in the thread. (The thread has some nice goodies in it for experts).

That x/twitter account has some beautiful physics (especially gravitation-related) animations on it. Worth scrolling through it.