[raattgift]

The apple sauce line is amusing, and I'm sure you know all the following, but even in Newtonian mechanics, potential and kinetic energies are frame dependent; for example the latter is rotationally but not Galilean invariant.

In modern gravitational physics you can treat components of the Einstein or stress-energy tensors as like these energies, e.g. for a family of observers, the apple-breaking kinetic energy is like the pressure components (T^ij, i=j, i!=0 ~ \gamma mv^2) and mostly in T^zz or T^rr or whichever, depending on one's choice of system of coordinates. However, simply by changing frame of reference, at each point where we find the apple/applesauce transition we can shuffle the whole of T^zz into one or more of the other components in G = T (keeping that relation invariant), and it is really stretching things to suggest that a change of coordinates is a process in the sense of the question in your first sentence.

> In general relativity black holes are not actually comprised of matter---they're entirely warping of spacetime

Well, that's not true of stellar collapse black holes; whatever you want to make of the trapping surface / apparent horizon, it encloses matter that existed before that formed. You don't need quantum anything, or even any future infalling, to deal with the fact that there is real matter inside at the time of formation.

The Schwarzschild vacuum solution is matter-free, but then astrophysical black holes of all masses and all origins generally do not truly source the Schwarzschild metric, just a usefully close approximation.

What you can say is that whatever's inside a black hole, eventually it will bald all its "hair" and can be effectively described (by an outside observer) at any point in time in terms of its spatial position (3 components), linear momentum (3 components), angular momentum (3 components), electromagnetic charge (1 component), and mass (1 component), with any other features irrelevant in the Kenneth Wilson sense. That is, eventually it doesn't matter whether it was all neutron degenerate matter or whether there were some other particles inside the horizon when it formed, but there was some matter there: the apparent horizon around V616 Monocerotis didn't just pop up spontaneously far from any matter.

Quantum gravity only matters if you want to make guesses about what state the matter is in within the horizon (assuming you're unhappy about it inevitably being crunched into an infinitesimal point as in classical General Relativity), or about what it looks like when during evaporation the horizon retreats far enough to expose that state. I'll assume you favour keeping unitarity in any solution to the AMPS firewalls problem, and would happily ditch the apparent validity of the EFT outside the horizon. :-)

[evanb]

Yeah, I went straight to the static solutions for simplicity of discussion. From the outside, though, is it even in principle possible to tell whether a BH is a stellar-collapse Bh or if it's an eternal Schwarschild vacuum BH? Now we're outside of my realm of expertise. Do I recall properly from my GR class that once stellar collapse begins the outer shell reaches the singularity in a finite time? In that case, I think it does come down to philosophy (if you're staying within GR) or some theory that resolves the singularity to say whether the BH is "made of matter" or not.

> I'll assume you favour keeping unitarity in any solution to the AMPS firewalls problem, and would happily ditch the apparent validity of the EFT outside the horizon.

You're damn right. Unitarity, unitarity, unitarity:

https://arxiv.org/abs/1602.01473 https://arxiv.org/abs/1603.03055 https://arxiv.org/abs/1606.04948 https://arxiv.org/abs/1606.04951 https://arxiv.org/abs/1709.01932

[raattgift]

Oh damn again, I should have looked at your links before typing, and figured out your connection to the papers, and saved on a rant. :-)

[raattgift]

> [several MCM papers with interesting bits and pieces that look worth more than a skim]

Wow you guys roll an awful lot of dice.

[raattgift]

> From the outside, though, is it even in principle possible to tell whether a BH is a stellar-collapse Bh or if it's an eternal Schwarschild vacuum BH?

There's a hint in "vacuum". There's real stress-energy and it's not where you would put it if building an exact BH solution by hand (I'll return to that in the last paragraph).

How do you tell if a body under a sheet has died peacefully in bed or was violently axe-murdered without lifting the sheet? Look for blood spatter.

If you see the daughter products of a failed core collapse supernova around a black hole, I think it would be strange to think, "hm, that black hole was probably there before the hot dense phase of the universe". The idea of a cosmic supervillain mischievously arranging nebulae around eternal black holes is amusing.

Isolated black holes are trickier, especially as masses go up. How does one distinguish between primordial black holes from early overdensities in the whatever was around at GUT scales or higher vs ones passes through the throats in in a cosmology like the Caroll-Chen model? Unless we catch them evaporating or until we spot them forming, I don't know. Spotting primordial formations is not hopeless, they can't all form with exact spherical symmetry or with the to-be-balded lumps and us on unfavourable alignments, can they? There's bound to be some larger (near-)extremal eating a smaller BH somewhere in our past lightcone. So even if they're very early we should see impressions of the extremal-with-lump gravitational radiation in the relic fields.

> Do I recall properly from my GR class that once stellar collapse begins the outer shell reaches the singularity in a finite time?

Yes, details in MTW section 32. Finite and fast by human wristwatch proper time.

> I think it does come down to philosophy (if you're staying within GR) or some theory that resolves the singularity to say whether the BH is "made of matter" or not

I think BH specialists would love it (and hate it) if someone found something in the matter sector that manifests truly enormous degeneracy pressure. Who knows what the heck is in the inner layers of neutron stars. Cutaway diagrams that show anything other than a ? near the core are wild speculations. One I saw that I enjoyed had six ?????? starting around 10^15 g cm^-3 just for emphasis. Unfortunately this wild hope gets ridiculously wild when considering the most massive known galaxy centre BHs, and eventually your explosion of question marks practically demand some quantum gravity (or asymptotic safety or something).

And anyway there are IR problems in quantum fields on general spacetimes. Even in extremely flat space, G = <T> easily blows up, and who knows what we'll see as we develop devices to point to the source of weak gravity. How small a mass can avoid being in an eigenstate of position for a brief test? [arXiv:1602.07539 is just the start of that story!]

And furthermore actually solving the EFEs is a pain and numerical methods are still barely an aspirin, and anyway readily leads one into even more ways to mislead yourself if you don't cling to a T-first approach instead of a g-first approach ('t Hooft put out a pretty crazy seeming argument based on a brute force diagonalization recently). Sure one could argue that "matter determines curvature" and not the reverse is at least partly a philosophical point, but practically, even if you start with a ridiculously improbable stress-energy distribution you won't be chasing down regions of spacetime in which the eigenvalues of T_ij have the wrong sign. It is perversely common that when one writes down a metric first and then add matter, you end up with a proliferation of negative energy density or find lots of tension around extended objects, or the like.

Tl;dr: I look forward to a successor to GR, but am pretty sure that whatever it is will be even harder to teach.