[evanb]

When an apple falls to the earth, by what process is its potential energy converted to kinetic energy? Gravitational processes alone.

Apple-earth collisions primarily radiate apple sauce, black hole mergers primarily radiate in gravitational energy.

Minor nit: In general relativity black holes are not actually comprised of matter---they're entirely warping of spacetime. Whether that remains true in a quantum theory of gravity is unknown.

[spuz]

None of this actually answers the question. The question is by what process does energy in the binary black hole system get converted into gravitational wave energy?

[T-A]

If you accelerate an electric charge, it emits electromagnetic waves. If you accelerate a mass, it emits gravitational waves.

Two masses orbiting their common center of gravity are undergoing centripetal acceleration, so they continuously emit gravitational waves, spiraling closer as they lose energy (that's how the emission of gravitational waves was originally confirmed [1]).

[1] https://www.nobelprize.org/nobel_prizes/physics/laureates/19...

[evanb]

The answer is "by the processes of general relativity". When things fall "down" their potential energy is lowered, so they get faster. When mass-energy accelerates it emits gravitational waves, in much the same way when an electron accelerates it emits electromagnetic waves. If you're satisfied that a radio works by sloshing electrons around, you should be satisfied that a black hole merger emits radiation by sloshing mass around.

Where did the photons "come from"? Well, they weren't stored "inside" the electrons. By what process were the photons generated? Electrons accelerating radiate. That's essentially the answer. You can "math it up" if you want. It's not exactly an axiom, but it's pretty close to the bottom.

[evanb]

Maybe I should be more clear: at least in the generally relativistic conception of gravity, all of the mass of the black hole "comes from" the warping of spacetime already. That's why I keep dancing around the question of whether it's "really" the kinetic energy or the mass or a mix that gets converted---it's hard to distinguish and may not be meaningful to distinguish the pieces from one another, especially if I go to a co-rotating frame.

[raverbashing]

> all of the mass of the black hole "comes from" the warping of spacetime already

No, it's the other way around. The warping is due to the mass

But the other answer hinted at the source: accelerating mass turns into gravitational waves as an accelerating electron turns into EM waves (remember rotation and things stopping abruptly also means acceleration)

So yeah, it's the potential energy that turns into (less than Newtonian amounts of) kinetic energy because some of it is turning into Gravitational waves

And you can imagine something as big as black holes spinning around each other at a frequency measurable in Hz how much energy they can give in that process then add the sudden merger deceleration.

[improbable22]

Certainly normal matter (like the earth) has mass and warps spacetime. But a black hole is a purely gravitational object, there need not be any normal matter involved.

The mass of a black hole is something that's really only defined from a distance away. If a planet of 1 earth-mass orbits it at the same speed & circumference as we do the sun, then we say the black hole has 1 solar mass.

[raverbashing]

> But a black hole is a purely gravitational object, there need not be any normal matter involved.

There's no "purely gravitational object" it only "looks like that" from behind the event horizon

We know the escape velocity > c and that's pretty much it, for GR it's a singularity (which usually means the theory is incomplete in that circumstance) and we don't know how QM work when squeezed harder than a Neutron star

> The mass of a black hole is something that's really only defined from a distance away.

If you mean "we can sense the gravitational field of something having mass X at a distance D larger than the event horizon" I agree.

But I'd rather say "we don't know what happens there" instead of "singularity" (which is what the current theories say it's inside and from the point of view of Relativity they're not wrong)

[raattgift]

> But a black hole is a purely gravitational object

Are you calling compact objects from stellar collapse that have an apparent horizon something other than a "black hole"?

> The mass of a black hole is something that's really only defined from a distance away

The stress-energy in the region of spacetime where one finds a black hole totally determines the Einstein tensor in that region. Solve the Einstein Field Equations for T_munu in \Sigma \subset \M. Extract the metric tensor. Solve the geodesic equations for that region, and you have the orbit for your Earthlike planet. You can make it simpler and consider the surface stress-energy on a shell within the horizon, or even outside in the case of your orbiting Earthlike planet problem, for which we don't care about the region inside the shell.

You are skipping the first steps, treating the metric tensor as a known, or worse, something that you can extract from a single geodesic.

But let's think about that anyway. Do you really know the metric you source? Sure, your stress-energy is localized so you can deploy a large shell to partition the "inside" and "outside" stress-energy. "Outside" it's zero, and nobody will really care about your small deviations from exact spherical symmetry, so your metric is therefore Schwarzschild, right? No, we can't make that inference based on the far field outside the shell; we need an Israel junction condition. [Synge 1960, Relativity: The General Theory (Amsterdam: North-Holland), ch. IV § 6 goes into this in detail, contrasting "realist" vs "agonist" and "creator" positions; yours is the "creator" position in that you are happy with an exact solution of the EFEs, and so you might enjoy reading what Synge wrote as he walks towards the mathematics of junctions :-) .] In a model can ignore that because we get it "for free" by laying down an exact generator of the vacuum Schwarzschild solution and not worrying whether the stress-energy is physical.

[raattgift]

Heh I should have kept reading down the thread, could have saved some typing. :-)

[evanb]

I thought your other answer was great!

[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.