Edit: maybe because these two forces have very different magnitude it is not possible to measure it
In fact gravity is even self-interacting with itself. ie. Gravitational fields themselves influence the propagation of gravitational fields. If this wasn't the case we'd observe gravitational waves from distance objects earlier than the speed of light. Which would be a problem for all our current models of physics if true.
Generally the space between us and distant objects isn't actually a perfect vacuum. It should have an index of refraction greater than 1, and it should vary by frequency. Light from a distant object should arrive here spread out in time by frequency, and the earliest should arrive a little later than something moving at the speed of light would arrive.
Is there something like the index of refraction for gravity waves? If not then we should see gravity waves from an event before we see any light from the event. If there is, then it should be possible for gravity waves to arrive before, at the same time, or after light from the same event depending on the frequency of the gravity wave and the light.
We have measured the relative speed of gravity and light. The difference is constrained to be no more that about 10^-15 times the speed of light. This us based on a signal that travelled 130 million light years.
Of course going faster than light which is being slowed by absorption and re-emission isn't the same as breaking the speed of light since light itself is going slower than the speed of light in this case.
So yes you're right that it isn't exactly the same arrival time but we're not talking about curvature differences here, we're talking about physical interactions that the light undergoes that gravity doesn't.
That said, I’m still trying to come to terms with the fact that breaking this speed limit just means that causality would be potentially broken. Isn’t that just something we axiomatically believed based on experience and we just haven’t observed otherwise?
Because of how the three dimensions of space and one dimension of time are put together, you can think of there being a balance or trade between motion in space and motion in time. If you aren't moving in space, you're moving through time at the maximum possible "rate". The more rapidly you move through space, the slower you move through time. This trade bottoms out at "c", at which point you're not moving through time at all. (Since motion is impossible without time passing, "c" itself is unachievable; you can only approach it asymptotically. Something about massless particles makes "motion" not a thing in the first place, I think, meaning they can actually propagate at exactly "c" as seen by an observer.)
You can visualize this as a dial on an X-Y graph which starts out pointing in the Y direction, and as you speed up, it turns more toward the X direction. When you're pointing completely in the X direction, you're moving "at the speed of light", purely in space and not at all through time. If you turn the dial even further, you're trading some of that speed back for motion in time... but in the opposite direction.
Of course, this is all super-handwavey; most importantly, velocity has to be measured relative to an observer, so all of this about rates has to be anchored relative to an observer. (But this is also precisely why massless particles propagate at the same rate regardless of observer -- insert timey-wimey Doctor Who reference.)
Greg Egan has a lovely trilogy, Orthogonal, set in a universe where space and time don't have this trade (formally, the sign on the time variable in some critical equation is flipped to match the spatial dimensions). He has some great material on the exact physics of such a world. [0]
Maybe the gravity emanates from outside the event horizon, but then why would it pull us inside?
Thanks
>The final conclusion of our analysis is that there appear to be no physically acceptable stable solutions of the MTZ system
https://arxiv.org/pdf/0710.1735.pdf
Basically it's a huge hole in black hole theory right now. It should be made clear though that both gravity is self interacting and black holes do exist. It's just when you get down to specifics it's a case of "we don't know how to make this work".
I assume punching a hole in spacetime, punches an equivalent hole in maths aswell
Let me ask a few simpler questions first, my main question is at the end
This punched hole might be like measuring angles with a differential. When the difference between the measured points hits zero, the other end of the equation hits infinity and the angle becomes meaningless
So would a true vertical curvature in spacetime equivalently require an infinite amount of mass?
They say that at the event horizon the deformation is so strong that from a black hole all paths lead inwards. But isn't gravity commutative? A.k.a. coming from inside, vertical curvature is reached. But if the curvature is vertical, then presumably there is also no way into a black hole?
---
So main question; could we just say that vertical curvature is impossible, and black holes are simply extreeeeme curvature to the extent that a 1.7second difference between light waves and gravitational waves over 130million years is enough to stop light escaping, but not gravity?
Is that solution too simple, what am i missing?
Thanks
Instead since light is redshifted as it exits a gravity well a better thought would be "is the almost but not quite black hole red-shifting light to the point of being impossible to detect?". After all light with almost 0hz frequency is basically non-interactive. It has a similar outcome. You could then have an 'almost black hole' that looks just like a real black hole but allows gravity to escape. https://arxiv.org/abs/2102.07769
> You could then have an 'almost black hole' that looks just like a real black hole but allows gravity to escape
I wondered if that answer to the conundrum could apply to all black holes. I suppose not
For real black holes, I suppose we should say they are not true singularities where the event horizon curvature goes vertical, but simply that curvature goes beyond the speed of light, so the maths still makes sense
Thanks that is a lot more logical
So then the effect of gravity from a real black hole would be like the effect of a messy person after they've left the room, and the reason why the effect of a black hole is felt for much longer is because of time dilation, and gravity doesn't experience redshift?
> astro-ph/2102.07769
This is about a particular model of dark matter that unlike in the standard cosmology is hot and has a particular radial profile within galaxies and outside galaxies undergoes a phase change to a uniformly distributed cold dark matter.
Tracing the gravitational collapse consequences of a theory whose characteristic matter distribution does not concord with observation (it breaks when the radial symmetry breaks, as in galaxy-galaxy mergers, lumpy galaxy clusters, and so on) is interesting but doesn't say much about astrophysics.
The preprint itself was the basis of a workshop talk on speculative physics, and the workship was literally titled in the form of a question ("What Comes Beyond Standard Models?")
FWIW, I had never before this heard of Bled Workshops in Physics, and I still don't know (after poking around in citeseer and the like) whether it is an event in Slovenia, or just named after Bled, Slovenia.
> hep-th/0710.1735
I don't understand why this is in hep-th rather than gr-qc as it is manifestly about a semiclassical model, with a peculiar form of quantum matter used to study gravitational collapse.
The paper is essentially an obituary for an idea for a toy quantum field on a classical curved spacetime that might work better than the simplest toy quantum field that has been in use since at least Hawking's 1974 work. The original work [hep-th/0205.319] introduces this toy model containing analogue to electromagnetism, and found that they could only form black holes under certain conditions. These additional complications, your linked paper's authors argue, aren't helpful even under those certain conditions, leading to things like naked singularities away from the horizon (p.20).
The paper's central purpose is to narrow the viability of this family of toy matter; in the authors' words (p.2.), "In this work we address the following question: Are there other static, spherically symmetric black hole solutions for the MTZ model, satisfying the dominant and strong energy condition between the event and cosmological horizon, besides MTZ1 and MTZ2? Using a combination of analytical and numerical methods we conclude that the answer to this question is negative." (In the very next paragraph they point out that MTZ2 has already been shown to be unstable with the addition of spherically symmetric masses, and that they will show that MTZ1 has the same problem).
The final paragraph of p.20 is pretty damning, and declares the low-energy-string-theory MTZ idea dead. ("M" is also one of the authors of the obituary). And so this raises my second question:
Why did you link this paper?
In my view does not support your statement that there is "a huge hole in black hole theory right now", but am certainly interested on what motivated your choice of that paper in the context of the questions tsegratis asked. Neither paper seems to go anywhere near answering those questions.
Lots of answers at link, most amusing one is:
> The total mass of the black hole must reside, completely, and only, in the self-energy of the curvature of spacetime around the hole!
> The answer to your question, then, is this: information about the mass of a black hole doesn't have to escape from within the black hole because there is no mass inside the black hole. All the mass is distributed in the field outside the hole. Therefore, no information needs to escape from inside
It seems the general answer is that fields and particles are not the same thing, and black holes can generate fields...
Since time stops within a black hole singularity, is entering one a good tip for escaping the end of the universe?
Below is some interesting background, on how a field is static, already defined at the creation of the black hole, and particles, if they happen, are just communicating changes in the field:
> A particle is an excitation of a field, not the field itself. In QED, if you set up a static central charge, and leave it there a very long time, it sets up a field E=kqr2. No photons. When another charge enters that region, it feels that force. Now, that second charge will scatter and accelerate, and there, you will have a e−−>e−+γ reaction due to that acceleration, (classically, the waves created by having a disturbance in the EM field) but you will not have a photon exchange with the central charge, at least not until it feels the field set up by our first charge, which will happen at some later time
> Now, consider the black hole. It is a static solution of Einstein's equations, sitting there happily. When it is intruded upon by a test mass, it already has set up its field. So, when something scatters off of it, it moves along the field set up by the black hole. Now, it will accelerate, and perhaps, "radiate a graviton", but the black hole will only feel that after the test particle's radiation field enters the black hole horizon, which it may do freely. But nowhere in this process, does a particle leave the black hole horizon
> On 2017 August 17 a binary neutron star coalescence candidate (later designated GW170817) with merger time 12:41:04 UTC was observed through gravitational waves by the Advanced LIGO and Advanced Virgo detectors. The Fermi Gamma-ray Burst Monitor independently detected a gamma-ray burst (GRB 170817A) with a time delay of ∼1.7 s with respect to the merger time.
So there is a delay between arrival of gravitational waves and accompanying gamma ray burst, but I couldn't tell you if that's purely because light travels slower than it would in a perfect vacuum, because the gravitational waves are generated before the gamma ray burst, or a bit of both. The GRB being less than two seconds long, I would guess they both happened at close to the same time, and it does have a speed difference.
Coming from an object 130 million light years away, 1.7 seconds is a very small difference in speed.
If there was something that didn't obey fundamental changes to spacetime itself we'd observe things like gravitational waves in a completely different location and time to their visual counterparts. We do not see any evidence of this. So for any theory that states a change in the fabric of spacetime itself you can guarantee that everything must conform to that change.
This is a handy feature, since when a high-redshift candidate event is detected by LIGO or Virgo, various telescopes can search the inferred location on the sky, looking for a trailing component. A neutron star-black hole merger, for instance, will have a such a component. So will a star falling apart in proximity to a black hole (a "tidal disruption event"). The spread for closer events isn't so big: detection of the LIGO/VIRGO G298048 (sourced about 140 million light years away, so very low redshift) event's gamma rays trailed by about about 1.7 seconds after the gravitational waves.
We can draw a direct comparison with neutrinos. Although they are not massless, and thus obey a different wave equation, they are very very very light, so we in multi-messenger astronomy we can treat them as if they effectively move at the speed of light. (In fact, supernova multi-messenger astronomy is a strong constraint on the difference between the speed of light and the speed of neutrinos).
Neutrinos also couple with gas and dust very very weakly, and so a neutrino signal and a gravitational wave signal will arrive at nearly the same time, with the electromagnetic components arriving later.
> ... curvature ... curvature of spacetime ... Gravitational fields themselves influence the propagation of gravitational fields
While you're right that different solutions of the Einstein Field Equations of General Relativity do not superpose linearly (around a Schwarzschild black hole, a very low-mass particle behaves very differently from a one with enough mass to have a gravitational self-force: https://arxiv.org/abs/0902.0573 for gory details) it's probably easy to be misled by mixing a field view of General Relativity ("GR") with a geometry ("curvature") view.
We can take an effective field theory view of GR and say that there is some chosen background (e.g. Minkowski spacetime) that is perturbed by a non-rotating point mass, the combination of the two (Minkowski + perturbation) generates the Schwarzschild spacetime. We can then add another mass, a second perturbation, and see what the combination of three (Minkowski + perturbation_1 + perturbation_2) does. This is the approach of https://en.wikipedia.org/wiki/Post-Newtonian_expansion and as can be seen in the diagram on that page, it is only valid when the two masses are fairly far apart. It is hard not to think of the perturbations as fields in the sense that you seem to be thinking about. Unfortunately this has its limits. As you bring the masses closer together (increasing compactness, moving downwards on the Y axis in the diagram), obviously wrong predictions tend to creep in, destroying one's confidence in the idea that in a system with multiple gravitating masses, each generates its own independent gravitational field which can somehow be combined (or which somehow propagate through some background).
In the most popular General Relativity reference book, Misner, Thorne & Wheeler's Gravitation, the authors discuss the expression "prior geometry", meaning some aspect of the curvature which is externally fixed or non-dynamical. General Relativity is a theory with "no prior geometry", and they make a brief argument about this. While some decades later we are much better with post-Newtonian expansion approaches (which do fix a prior geometry, which is then studied using perturbation methods), and can ignore "no prior geometry" as much more than a slogan in many cases, unfortunately we cannot do so for all of them.
For highly relativistic problems (objects moving near c; "escape velocities" near c), one must resort to the full theory of General Relativity, either solving the exact form, a good approximation (see https://pos.sissa.it/081/015/pdf), or a numerical solution where neither of the previous two forms are known or to "hide" divergences in analytical approaches.
Additionally, for speculative modelling of highly relativistic systems we may wish to require that the model enjoy the manifest https://en.wikipedia.org/wiki/Background_independence of the full theory of General Relativity, which in a practical sense means that all possible observers will agree on the point-coincidences of the system independent of the choice of observer's system of coordinates or relative motion (object "A" and object "B" are in contact at the same point in spacetime for all observers; you don't have fast-moving observers calculate them never to have been in contact; you don't have rotating observers calculating them as never-in-contact; you don't have observers in deep space disagreeing with planet-bound observers about whether "A" and "B" come into contact, etc).
Approximations instead fix some aspect(s) into a background, and in some strongly relativistic systems, one may have to introduce counter-terms ("ghosts") for families of observers that are not ideal Eulerian observers within that background.
(Einstein has a good argument about this in Chapter XXXII ("The Structure of Space According to the Theory of General Relativity") in his 1934 book, https://www.ibiblio.org/ebooks/Einstein/Einstein_Relativity.... whose "not-even-quasi-Euclidean" argument is extended in Appendix 4 and accompanied by a further fourteen pages as Appendix Chapter 5 ("Relativity and the Problem of Space") in the (not-as-freely-available) 2nd edition https://doi.org/10.4324/9780203518922 )
… or something like that.
Do note that current quantum field theories do not work in curved space-time, so this may turn out to be wrong in certain crucial ways.
In general curved spacetimes. But that includes a lot of obvious unphysicality.
Modelling our universe, QFT in CS (the subject of textbooks, after all, like Birrell and Davies) works just fine away from strong curvature, all of which as far as we can tell is shrouded behind an event horizon or not-practically-observable in the very early universe.
You don't have to take my word for it. See https://en.wikipedia.org/wiki/Robert_Wald 's first three slides (after the title slide) at http://gravity.psu.edu/events/abhayfest/talks/Wald.pdf )
tl;dr: it is a fine effective theory, but not a good candidate for a fundamental theory.
(Also in your first paragraph you are implicitly carving up spacetime in to space + time, and not taking that into account in what you write about "straight lines". However, you've got one part right namely (paraphrasing the start, up to the second comma, of your parenthetical) the spacetime interval of a null geodesic).
It's a matter of perspective. Our Solar System's mass is 98% in the Sun. Earth is tiny and small and, as a GR object, is moving very slowly, and that only according to how its particles were set in motion at the beginning of time.
As others have said, gravitational lensing is a real thing, but that is a cosmological effect, and we are completely at the whim of the Initial Conditions for these opportunities.
(If there are real engineering applications for GR, especially in optics, I would be delighted and grateful to learn more!)
Large-frame optical Sagnac gyroscopes for precision geodesy:
https://www.frontiersin.org/articles/10.3389/fspas.2020.0004...
And some detail on the GINGER project, "Sagnac Effect, Ring Lasers, and Terrestrial Tests of [post-Newtonian] Gravity" (clarification mine), https://www.mdpi.com/2075-4434/3/2/84/htm
I imagine there is some literature on higher order modes in dispersion compensating fibre spools placed over underground flows (magma, water) but don't really have time to think about what decade practical engineering problems might emerge.
Of possible interest to you, quoting preface of following: "These few words should make it clear that quantum optics, experimental gravitation and measurement theory are not nearly as far apart as one might first have thought. However, there has traditionally been little contact between physicists working in these various fields." (which is a little less true now because of e.g. LIGO) https://link.springer.com/book/10.1007%2F978-1-4613-3712-6
Next, I'm pretty sure that the emissions spectra of galactic magnetars (https://en.wikipedia.org/wiki/SGR_1935%2B2154 , one of Arecibo's last big detections, §2.1 of https://arxiv.org/abs/2103.06052v1 ) are far from the cosmological scale (see https://arxiv.org/abs/1507.02924 n.b. figure 24).
> gravitational lensing ... is a cosmological effect
Also pretty sure the Magellanic Clouds, other non-naked-eye Milky Way satellites, and some galactic targets aren't "cosmological", https://en.wikipedia.org/wiki/Gravitational_microlensing#Obs...
Finally, it strikes me as unfair to to invoke Initial Conditions as a way to discount the relevance of gravitational observations. What, if not Intial Conditions, determines the frequency of your HeNe laser? Where did the neon in particular come from? (spoiler: https://en.wikipedia.org/wiki/Neon#Occurrence) And that helium is mostly a cosmological effect! ("The vast majority of helium was formed by Big Bang nucleosynthesis one to three minutes after the Big Bang. As such, measurements of its abundance contribute to cosmological models.")
Strong evidence that God loves helium, and considers it a good party trick to have some on hand! But I always thought He was generated from fusing two H into an He in a Sun somewhere.