> 3.5 billion light-years from Earth
> mass falls between 10 and 100 million suns
The size of the sun already causes my brain to shut down. Everything about this is beyond contemplation.
> mass falls between 10 and 100 million suns
The size of the sun already causes my brain to shut down. Everything about this is beyond contemplation.
This intuition does not work in curved spacetime, particularly not for black holes. Black holes do not even have a well-defined volume at all.
I was uncomfortable with the conflation of the "volume of a black hole" with the volume of that sphere.
...is not what a black hole is. It is not even "something kinda sorta like a sphere with some Schwarzschild radius". It is nothing like any ordinary object you're used to. It doesn't have a well-defined "radius" any more than it has a well-defined volume; the Schwarzschild "radius" is actually sqrt(A / 4 pi), where A is the surface area of the hole's horizon (which in turn is calculated from the mass of the hole).
This is relevant to the discussion at hand because for these very large black holes that density is not very high and conceivably a gas cloud of sufficient mass could contract to that density and have an event horizon form without collapsing into Stars.
No, it doesn't. There are indeed upper limits on the mass of objects that are formed from stars that run out of nuclear fuel, before the objects collapse to black holes (the Chandrasekhar limit for white dwarfs and the Tolman-Oppenheimer-Volkoff limit for neutron stars), but those limits are not based on density.
It is true that, especially in the early universe, gas clouds forming very massive black holes without going through the intermediate stage of forming stars is considered possible; but that is not based on the kind of simplistic calculation that you describe. It's based on numerical simulations of the Einstein Field Equation with relevant initial conditions.
Another factor you are not considering is that the universe is expanding, and the early universe was expanding much more rapidly than our current universe is. So gas clouds contracting to form very massive black holes had to work against the expansion to do so. That further complicates the calculations.
Is that correct? My understanding is that the expansion of the Universe occurs away from large concentrations of mass; expansion doesn't cause the stars in a galaxy to move apart.
What does that mean? The Schwarzschild radius is just the distance at which even light can no longer escape, the only matter there is the matter that happens to be falling in at that moment. Unless you mean the average density within the Schwarzschild volume (a term I just made up as far as I know, but you know what I mean) if all the mass of the black hole were spread out evenly throughout it.
That seems like a weird condition. "Average density" is pretty well-defined and doesn't need even spreading.
Even more, isn't the distribution of mass within a black hole a meaningless question? There's no information coming from the black hole, for an external observer it literally doesn't matter how the matter is arranged within.
A rotating (or merging) black hole can be deformed (non-spherical), but that doesn't stop you to calculate average density.
It's not really separate, because more things can fall in.
It's also not really separate if black holes may evaporate, in part because it is the outside conditions that determine when (and even if) evaporation begins. There are unsettled questions about whether black holes, even given suitable exterior conditions, fully evaporate; and exactly how to connect what fell into the black hole with what's left after complete evaporation. However, it is the mass inside that gives rise to Hawking radiation outside, so there is some connection.
Otherwise I think you're quite right, particularly about the gentleness of the Weyl curvature (the tidal part of the Riemann curvature tensor) around the event horizon of a large black hole.
"Pass through the event horizon, alive" is the "no-drama conjecture" that is part of the firewalls debate. Indeed, extremely massive black holes should have the least drama in the classical theory which describes black holes in the first place, so what feature of some quantum theory generates extremely high energy particles that we don't find anywhere between the Earth and Moon, or in the Jovian system, etc? "The firewall radiation can only be seen upon crossing an event horizon and there isn't one in those parts of our solar system" is not very satisfying, and it turns out that the arguably best-developed answer to that (by Afshordi/Dykaar/Abedi) is not significantly supported by gravitational wave data (so called repeating damped "echoes" cannot reliably be extracted from the noise) from LIGO, Virgo, and Kagra so far.
Though they might just be mathematical abstracts and not "real".
https://en.m.wikipedia.org/wiki/White_hole
https://physics.stackexchange.com/questions/740527/penrose-d...
A longer answer is somewhat model-dependent, and somewhat on how one chooses to split spacetime to distinguish spatial distances (for volume) and time (the volume is time-dependent). Unfortunately this means thatg for practicaly any given black hole there is no unique definition of its interior volume.
In general it is fairly safe to say that within generic black holes there is a small volume that tends towards infinite density, and that small volume is embedded in a much larger (even for a tiny-mass black hole) interior space, even fairly early in the (time-dependent) black hole's lifetime (e.g. within a few horizon-diameter light-crossing times after formation by matter collapse).
The most commonly known theoretical models of black holes are, absent perturbation, not time-dependent. This tends to highlight the non-uniqueness of interior volume. DiNunno & Matzner 2008 <https://arxiv.org/abs/0801.1734> is a fine pedagogical treatment. 'An occasional question to the teacher of relativity is: ".. then what is the volume of a black hole?" The answer is that, unlike the response about the surface, the volume depends on the way that the 3-dimensional "constant-time" space containing the black hole is defined.'
I have a memory of a fine and surprisingly accessible treatment by a mathematician about the interior volume of a Schwarzschild BH, but unfortunately I can't find the URL. There are plenty of other discussions about BH interior volumes scattered around the web and the academic literature, although a depressing number of the latter focus on anti-de Sitter (AdS) black holes. Black holes in our universe, like the one in the linked Chandra article or like Phoenix A, are decidedly not embedded in a collapsing spacetime with a lightlike boundary "screen" as would be the case if the exterior spacetime of these black holes were AdS rather than expanding Friedmann-Lemaître-Robertson-Walker with local overdensities (the galaxies around these black holes). Which is too bad, because if our universe were AdS, the interior volume of a black hole could have a nifty relationship with information complexity; in our universe, shrug.
Two more things for completeness. The exterior of a black hole, if not vacuum, can be relevant in determining the interior volume. Single black hole exact solutions (Schwarzschild, Kerr-Newman) have infinite vacuum outside the horizon, but one can introduce perturbations (lumps of matter or other mass-energy) that raise "bumps" on the horizon and strangenesses in the interior. For a large and relativistic perturbation like a second black hole, or a swarm of them, you run into the problem that in general single black hole solutions do not superpose well (and certainly not linearly). The interiors of "hard" black hole binaries may be very different from that of black hole binaries so soft (or wide, thinking only spatially) that they are barely in mutual orbit. And finally, black holes may evaporate completely, so the spacetime would then be finite, and thus it would be weird to cut the interior spacetime up into time-indexed spatial volumes where some of those volumes are infinite.
Consequently, calculating an average density comparable to that of a homogeneous ball of fluid (or even a differentiated planet like Earth) doesn't really say much about the black hole itself. And that I think is the weird thing related to your comment.
Finally, even for round-planet-sized objects and stars, the interior volumes "suffer" a mainly mass-dependent volume surplus compared to a Euclidean 3-ball. The interior Schwarzschild solution is a starting point; it provides a calculation for the volume of a self-gravitating sphere of a constant-density fluid or gas and this calculation reveals that that volume is greater than the corresponding empty spherical shell <https://en.wikipedia.org/wiki/Interior_Schwarzschild_metric#...>.
One could argue that Plank length is not the most best lower limit.
It turns out, as beings living in the 10^0m scale, we are much closer to the size of the universe 10^27, than to the smallest possible distance, 10^-35.
Which boggles my mind, I did not imagine the Planck length to be this small, if it even makes sense to use the word "imagine".
It has nothing to do with smallest possible length or something like that and it's just a common mistake in non-scientific physics articles that has sadly spread.
From the article:
> The extremely distant black hole is located in the galaxy UHZ1 in the direction of the galaxy cluster Abell 2744. The galaxy cluster is about 3.5 billion light-years from Earth. Webb data, however, reveal that UHZ1 is much farther away than Abell 2744. At some 13.2 billion light-years away, UHZ1 is seen when the universe was only 3% of its current age.
In fact Earth might survive (as an ice planet) much longer than it would around the Sun since the Sun is expected to become a red giant and possibly swallow the Earth when it dies.
And as a motivator for both our intellectual curiosity and our scientific curiosity, the lack of a detailed moon in our night sky would have retarded the development of human civilization.
On another note, our senses generally work on a log scale (https://en.wikipedia.org/wiki/Weber–Fechner_law), so it’s not something unnatural.
Where confusion creeps back in is when sensory input is quantified. People don't perceive a 1000 lumen source as twice as bright as a 500 lumen source, but tend to think they should.