The question is broad, and we still don't know what is quantum gravity. But let me be more specific.

In the question (on this site, see below) on whether gravitational waves have entropy the answers were that it could, but typically a small quantity, or perhaps none at all when a solution of the Einstein equations. Much thanks for the answers to Peter Diehr, Lawrence Crowell, and wetsavannaanimal-aka-rod-vance.

See: Do gravitational waves have entropy?

However, the discussion was in the realm of classical General Relativity (GR), with no quantum effects. The question excluded Hawking radiation type effects also. The question here is whether the results are different if we take quantum gravity into account (not just quantum fields in classical gravity)

In classical GR it was thought that black holes have no entropy, or very little, because of the no-hair theorem. Gravitational waves, classically, which interact very weakly with matter (like any gravitational field), would thermalize very slowly and thus acquire little randomness to have much entropy (using a Shannon or statistical mechanics measure of entropy, or so it seems on intuitive/physical grounds). The degrees of freedom that the gravitational waves could statistically have, say for the gravitational radiation emitted by the merging black holes (BH's), and detected in 2015 by LIGO, is not obvious, but classically it does not look like much. The waves seem to be a pretty well defined (even if we don't calculate to all orders) by the two black holes parameters. See Ref 1 for discussion and answers which explain it much better than I could, and which seemed to me to be approximately correct.

The question is whether the same would be true taking quantum effect into account. This question was suggested in that other question, by wetsavannaanimal-aka-rod-vance.

Even though BH thermodynamics (ie, end entropy >= initial entropy, and the BH entropy/mass/area equations) hold up consistently (from the observed data and deductions), it is interesting that the 3 solar masses, which when they were part of the BH contributed to a maximum measure of entropy, after radiation seem to be contributing much less. Of course, the total entropy is still more, so no physics was violated. Possibly some amount of entropy could be involved in the angular momentum of the gravitational waves (some must have been radiated away), but again that seems to have been a pretty deterministic process, not clear where a lot of randomness could come from.

So the question is, could the entropy be much different when taking quantum gravity into account?

One possible option could be whether there is anything that could be concluded from the AdS/QFT correspondence and the holographic conjecture, or a calculation from it? -- this was suggested clearly bywetsavannaanimal-aka-rod-vance in his comments, but the wording (and any misunderstanding) is mine

Or would somehow the strong gravitational field that created the gravitational waves during the merger (all 3 phases, mainly in the strong field region) really need to include its effects on quantum gravity fields (but we're not at the Planckian scale yet, so probably not)?

If that gravitational radiation was somehow focused some and a large part absorbed by a larger BH (so that it has a significantly smaller lambda than the size of the larger BH and the cross section is higher (there are papers on absorbing grav radiation by a BH, very lambda and geometry dependent, also spin, but even no spin will absorb), the BH entropy (and area) would have to grow because of the mass-energy of the gravitational wave absorbed. That certainly provides a max to the entropy the gravitational wave can carry (easy, same as a BH with its mass), but it does not provide a minimum.

Is there anything one could conclude or suggest with our current understanding of quantum gravity and/or the overall physics?

  • $\begingroup$ You can calculate the entropy of the gravitational wave from its waveform and it is miniscule. I think you are mistaking the potential channel capacity of gravitational waves, which is just as large as the channel capacity of electromagnetic waves, for the actual content, which is small. Nobody denies that one could, theoretically, build a gravity based interstellar wifi-router. It's just that in practice one can't and nature doesn't. To go with Gertrude Stein: "Boring is boring is boring.". $\endgroup$
    – CuriousOne
    May 23, 2016 at 22:46
  • $\begingroup$ I@CuriousOne that was already asked and resolved in the question referenced. You might have looked. That was not the question, the question is whether including quantum gravity in the thinking makes any difference. Like I said, it does not look like it, but do we know, and what is the argument or rationale? It is absolutely NOT about channel capacity. $\endgroup$
    – Bob Bee
    May 24, 2016 at 0:02
  • $\begingroup$ Yes, if you quantize a classical wave, you lose possible information content because you can't dial the noise down arbitrarily low. At some point you hit the quantum limit. That's also a trivial insight from electromagnetism that transfer just fine to gravitational waves. May I make a suggestion? Stop treating everything that has gravity in it as something special. It's not special, at all and everything you know about waves form EM transfers just fine, assuming that you know how this works for EM waves? $\endgroup$
    – CuriousOne
    May 24, 2016 at 0:06
  • $\begingroup$ Your suggestion is not accepted, it is wrong as a fact. There are difference between nonlinear exact gravity (classically) and EM. Their quantum theories are also not the same, as you might read someplace, as gravity cannot be renormalized. Anyway, this is now probably beyond what these comments are meant for. $\endgroup$
    – Bob Bee
    May 24, 2016 at 4:22
  • $\begingroup$ There is no quantum theory of gravity and gravitational waves, at the moment, are a purely classical construct. Whether they even have a quantum aspect is unknown and will likely stay unknown for a long time. Like I said, you need to stop treating gravity as magic and simply apply what is already known. When you do, you will notice that gravitational waves are extremely boring. $\endgroup$
    – CuriousOne
    May 24, 2016 at 4:31

1 Answer 1


Nice question.

Gravitational waves are solutions of the linearized equations of motion and as such I don't expect quantum gravity effect to change in a significative amount the entropy content of the waves.

Nevertheless there are quantum gravity approaches, for instance the fuzzball proposal in string theory, where the discrepancy with classical physics is horizon-sized, so tiny differences in gravitational waves emission are expected. Indeed every fuzzball is different from another (fuzzball have microstates, while a black hole in general relativity is a single object with zero entropy from the microscopic point of view). At present there is still no realistic model in 4d (but people are working on this) and studying dynamical process is very diffcult, so it's hard to give quantitative statements.

What is radically different for sure is the way the information exit from the evaporated black hole, but this happens on a way longer timescale. In General relativity there is no way to do this, and the information paradox arises.

  • $\begingroup$ Thanks for your answer. The quantum gravity options for conditions that can be part of the generation of gravitational waves (GW). The horizon is one, and fuzzball model you say should predict some difference from GR GWs. You said TINY. I could guess it might, but could you say why tiny? And would they have entropy? Secondly, since fuzzballs have no horizons, could GWs from inside the fuzzball have entropy? I understand your statement that it's hard to do dynamical calculations, just wondering if there are any general statements that could be made on having quantum GWs with entropy $\endgroup$
    – Bob Bee
    May 26, 2016 at 1:05

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