The evaporation of charged black holes

[atyy]

"We present, for the first time, the full history of the evaporation of a large charged black hole."

https://arxiv.org/abs/2411.03447
The evaporation of charged black holes
Adam R. Brown, Luca V. Iliesiu, Geoff Penington, Mykhaylo Usatyuk
Charged particle emission from black holes with sufficiently large charge is exponentially suppressed. As a result, such black holes are driven towards extremality by the emission of neutral Hawking radiation. Eventually, an isolated black hole gets close enough to extremality that the gravitational backreaction of a single Hawking photon becomes important, and the QFT in curved spacetime approximation breaks down. To proceed further, we need to use a quantum theory of gravity. We make use of recent progress in our understanding of the quantum-gravitational thermodynamics of near-extremal black holes to compute the corrected spectrum for both neutral and charged Hawking radiation, including the effects of backreaction, greybody factors, and metric fluctuations. At low temperatures, large fluctuations in a set of light modes of the metric lead to drastic modifications to neutral particle emission that -- in contrast to the semiclassical prediction -- ensure the black hole remains subextremal. Relatedly, angular momentum constraints mean that, close enough to extremality, black holes with zero angular momentum no longer emit individual photons and gravitons; the dominant radiation channel consists of entangled pairs of photons in angular-momentum singlet states. We also compute the effects of backreaction and metric fluctuations on the emission of charged particles. Somewhat surprisingly, we find that the semiclassical Schwinger emission rate is essentially unchanged despite the fact that the emission process leads to large changes in the geometry and thermodynamics of the throat. We present, for the first time, the full history of the evaporation of a large charged black hole. This corrects the semiclassical calculation, which gives completely wrong predictions for almost the entire evaporation history, even for the crudest observables like the temperature seen by a thermometer.

 

[martinbn]

Do you have any thoughts or comments about it?

 

[ohwilleke]

"This corrects the semiclassical calculation, which gives completely wrong predictions for almost the entire evaporation history,"

This is an awfully confident statement to make about something that has never been observed, that may not even exist or be possible.

This is a particularly great instance of hubris given that this result is model dependent. While Einstein's field equations are very accurate in circumstances where it has been possible to test them precisely, there are lots of know possible, very subtle variations on them that are well-known in the general relativity research community which can not be distinguished from vanilla GR with existing observational tests. And, in this instance, the authors aren't even making the conservative choice of a vanilla GR model and are instead assuming one of many possible quantum gravity models.

Indeed, given the ambient temperature of outer space due to random background radiation and dust and interstellar gas, absorption of new matter-energy generally exceeds Hawking radiation for black holes that are stellar sized (roughly 2.5 solar masses plus or minus a quarter stellar mass), or larger. A "large charged black hole", by any reasonable definition of "large" won't evaporate completely at all, because a truly "isolated" large black hole isn't physical. There's basically no way that circumstances that lead it to form in the first place will leave it in a truly isolated state.

Maybe it is theoretically possible, but only in the same way that all of the oxygen molecules in your bedroom all ending up in your closet for ten minutes, until you suffocate to death in your bed, is theoretically possible in statistical mechanics. It is so profoundly improbable that it may have never happened even once in the entire history of the universe and it probably won't happen even once, anywhere in the universe, in another 140 billion years. It would probably take a long weekend to calculate that even remotely rigorously, but that is the kind of order of magnitude rarity we'd expect.

Only sub-stellar mass black holes (e.g., primordial black holes or laboratory created black holes) should lose more mass from evaporation than they gain from absorbing new mass-energy, absent really freak conditions that probably do not exist anywhere in the universe, even over time periods on the order of the current age of the universe. And, the expected lifetime of a sub-stellar black hole is closely related to its size. The smaller it is, the less long it lasts. Primordial black holes much smaller than typical asteroids by mass, if they ever existed, should be gone by now if they weren't lucky enough to eat enough new mass to grow faster than they are evaporating. So, again, even in the case of a "large" sub-stellar mass black hole, we are talking about a complete evaporation history that is tens of billions of years long that has a decent probability of being interrupted and reversed by mass-energy that it encounters now and then in that very long time period, e.g., because it collides with and eats a decent sized asteroid in a way that pushes it over the threshold of escaping future net evaporation.

Making bold predictions without data or a universally agreed model, about something that may actually be physically impossible as a practical matter, may be a consuming intellectual exercise, in much the same way as a game of chess against a skilled opponent or trying to memorize the first thousand digits of π. But it is an exercise that has little value, even as a way to advance our understanding of gravitational physics, and is meaningless as an actual prediction. It is right up there with the papers that theologians in the Middle Ages used to write about how many angels could dance on a pinhead.

The effort might have been a tolerable whimsy if it were a simple, manageable task to write (and for readers to read), but it wasn't. It's an illustrated novella with 106 pages plus appendices, and 19 figures. It was a substantial sustained time suck for four professional physicists. Sadly, it may even help each of them gain tenure. It isn't crank physics, and probably isn't even technically incorrect in any material way. But it so misses the forest for the trees, and so lacks any redeemable scientific value, that it is almost as bad as that.

If I were a gravitational physics journal editor, I would publish it only as a last resort. Many PhD dissertations (including Hawking's) are much shorter, yet add more value to the pool of scientific knowledge.

Overall two stars out of five for a physics preprint. Would not recommend.

 

[Demystifier]

Sadly, it may even help each of them gain tenure.

Some of the authors are already very accomplished:
https://scholar.google.com/citations?user=i0bK_soAAAAJ&hl=en
https://scholar.google.ca/citations?user=wHsmq4gAAAAJ&hl=en

 

[ohwilleke]

Some of the authors are already very accomplished:
https://scholar.google.com/citations?user=i0bK_soAAAAJ&hl=en
https://scholar.google.ca/citations?user=wHsmq4gAAAAJ&hl=en

FWIW, Luca V. Iliesiu is an assistant professor, which means he is tenure track but doesn't have tenure yet. Therefore, he is in publish or perish hell right now. Still, they are, and I didn't mean to imply that the were not, legitimate professional PhD physicists at reputable institutions. I am simply noting that their decisions about how to use their scarce resources of time for research are, IMHO, misdirected.

 

[mitchell porter]

the authors aren't even making the conservative choice of a vanilla GR model and are instead assuming one of many possible quantum gravity models.

They are extending the semiclassical model used by Hawking to deduce Hawking radiation, by a form of AdS/CFT ("JT gravity") that describes the wormhole-like throat around the event horizon, in order to describe the gravitational backreaction of the Hawking radiation on the black hole geometry (something neglected in the semiclassical approximation), which is necessary for this near-extremal black holes, because the emission of a single charged particle could push them beyond extremality, i.e. the electric repulsion due to the charge would exceed the gravitational attraction due to the mass, and you'd have a naked singularity rather than the usual "cosmic censorship" in which event horizons surround singularities.

They can use AdS/CFT because the geometry of the throat is AdS2 (an hourglass hyperboloid) times S^2 (it's sketched in figures 2, 11, 12 in the paper). It represents a quantum-mechanical approach to the "Schwarzian modes" that become relevant close to extremality. As these things go, it does seem to be a quite conservative way to think about this situation where the semiclassical approximation necessarily breaks down.

You say that complete black hole evaporation will never be observed because real astrophysical black holes are always finding new matter to consume. In the paper itself they say the scenario is artificial, not because of that, but because astrophysical black holes never come this close to extremality - there's always a mix of negative and positive charges in the matter they consume, so they don't get close enough to the maximum allowed charge, for the Schwarzian modes to become relevant. So it does seem that the best chance for these calculations to be physically and observationally relevant, is in micro black holes, whether primordial or artificial.

 

[ohwilleke]

astrophysical black holes never come this close to extremality - there's always a mix of negative and positive charges in the matter they consume, so they don't get close enough to the maximum allowed charge

I had actually considered mentioning that point as well (I only read the abstract and not the paper itself), but I figured that I'd said enough.

Also, could a "large" black hole even include a micro-black hole? I'm not clear how they operationalize the "large" condition for their analysis.

The topic of whether there are any naturally created micro-black holes in the universe today is indeed an interesting one. Conventional wisdom is that they could only be created shortly after the Big Bang and that most would have evaporated or ceased to be micro-black holes by now, 13.8 billion years later. We've pretty much ruled out primordial black holes as a source of a significant share of dark matter phenomena, even though the last few corners of the parameter space haven't been rigorously foreclosed yet. But that's a far cry from saying that there might not be a few of them out there somewhere, even though, so far, none have been observed (in part, because an isolated micro-black hole is intrinsically hard to observe).

I'd also be interested in the topic of whether it is possible to create a near extremal Kerr black hole artificially within even very ambitious technical limitations on human scientists. I'm not convinced that it is, but that would call for considerable expertise that I lack to say one way or the other.

I'd also quibble about whether any model that includes the possibility of wormholes is really "conservative", although perhaps I'm reading too much into a description of the "wormhole-like throat" that JT Theory allows in making that assumption. I'd agree that it isn't outside the mainstream of GR theory, but lots of GR theories are pretty wild.

I'd also continue to say, however, that even if JT Theory is a reasonable, and even a "conservative" choice among the available alternatives to a semi-classical approximation, that it isn't the unique and only possible model that one could use to analyze the situation. And, if that is the case, their statements are still awfully confident for a physically implausible, never observed, and model dependent conclusion in a situation where there is no one consensus model.

It would be one thing to say that: "This gives completely different predictions for almost the entire evaporation history than the semiclassical calculation, even for observables like the temperature seen by a thermometer," and it is quite another to say, as they do that:

This corrects the semiclassical calculation, which gives completely wrong predictions for almost the entire evaporation history, even for the crudest observables like the temperature seen by a thermometer.

This final quote is part of what really gives the paper its angels dancing on pinheads feel. Because it is basically impossible, and because we aren't really certain what the correct model to use in this circumstance is, there is no such thing as a "correct" answer to the question they purport to answer.

 

[ohwilleke]

If I were trying to make the case that this paper was worthy of publication to journal editors and represented my academic merit to a tenure committee, I'd spin its significance very differently with something like this that emphasized the quantum gravity methodology used and not the correctness of the result in the improbable situation modeled (with nine fewer words than in the current abstract and seven more words in the title):

A quantum gravity proof of concept model of the evaporation of charged black holes

The semiclassical approximation of general relativity used to explain Hawking radiation has a limited domain of applicability. For example, when a charged black hole gets close enough to extremality that the gravitational backreaction of a single Hawking photon is important, the QFT in curved spacetime approximation breaks down.

One alternative to Hawking's semiclassical approximation is a quantum gravity theory called "JT Theory" (JT). It can fully model systems that are challenging for a semiclassical approximation (e.g., a toy-model of the full evaporation history of a large, isolated, near extermal charged black hole, where gravitational backreaction, greybody factors, and metric fluxuations are significant) without breaking down. JT made it possible, for the first time, to model the full evaporation history of a large charged black hole, something no other theory has achieved.

Using JT, at low temperatures, large fluctuations in light modes of the metric drastically modify neutral particle emission ensuring that the black hole remains subextremal. Also, due to angular momentum constraints close enough to extremality, black holes with zero angular momentum no longer emit individual photons and gravitons. Instead, the dominant radiation channel consists of entangled pairs of photons in angular-momentum singlet states. Somewhat surprisingly, however, the semiclassical Schwinger emission rate is essentially unchanged, even though the emission process leads to large changes in the geometry and thermodynamics of the throat. JT makes completely different predictions than the semiclassical calculation for almost the entire evaporation history, even for observables like the temperature seen by a thermometer. The magnitude of these quantum gravity effects shows the importance of modeling systems like this one with a fully quantum theory of gravity.

With this spin, the paper comes across as having a lot more academic merit as a rigorous proof of concept of a particular quantum gravity model, that can be applied in other more realistic circumstances in future papers. Before, it came across as a purely hypothetical analysis of an impossible scenario that breaks down into a "who would win in a fight between Superman and Dr. Strange?" type comparison of the semiclassical approximation and JT Theory that it is impossible to resolve definitively.

Obviously, the tone of the introduction and results/conclusion sections would also have to be reworked along the same lines.

 

[liliesiu]

Hi, I am one of the authors of the paper.

I received an email from one of you asking me to comment on this thread and thought it would be good to clarify some points of confusion. The calculation done in the paper is independent of how you UV complete quantum gravity - rather, it is an effective field theory calculation that starts with GR coupled to a QFT (the standard model for most of the paper) and answers what the quantum fluctuations of the metric and QFT fields look like around a given black hole geometry. In the past, people thought that for macroscopic black holes all fluctuations are suppressed, i.e. that the geometry looks pretty much classical physics predicts. What we realized in the past couple of years is that this incorrect for black holes close to extremality (at very low temperatures) - there are a subset of modes of the metric whose fluctuations are arbitrarily large (they scale with the inverse temperature of the black hole). At the level of an effective field theory these modes have an action that is identical to that of JT gravity. Thus, JT gravity is not a toy model in this context; rather it is a tool with which we can quantitatively understand the large fluctuations of the metric in black hole geometries close to extremality. I'll put it another way. Any UV completion of quantum gravity should only mildly modify the EFT (for instance through the presence of small higher-derivative corrections in the gravitational action); such modifications turn out not to affect the presence of the modes of the metric that have arbitrarily large fluctuations at low temperatures. This implies that our results are universal. If tomorrow you come up with a UV completion of quantum gravity that can compute the spectrum of black hole microstates and the spectrum of Hawking radiation for such black holes, reproducing the EFT predictions that we make would be a non-trivial consistency check of your proposal.

(A side-note: similar consistency checks were proposed by looking at much smaller quantum corrections to the entropy of Schwarzild black holes: https://arxiv.org/abs/1205.0971
As it turns out, loop quantum gravity made predictions for such quantum corrections that were inconsistent with the EFT prediction. The only way out for loop quantum gravity would be to correct these predictions or explain why for this specific calculations EFT breaks down. I don't know whether loop quantum gravity researchers revisited these corrections after Sen's paper appeared.)

This brings me back to describing the concrete results and additional motivation for our recent paper. The main goal of the paper is to find the consequence of such large metric fluctuations for the radiation that such black holes emit. This is important because Hawking's standard calculation clearly gives problematic answers for such geometries. For instance, Hawking's calculation predicts that a single Hawking quantum can take the black hole geometry from being sub-extremal, to being super-extremal. Super-extremal geometries are highly problematic: the horizon of the black hole disappears and the geometry has a naked singularity. People realized this problem 30 years ago (see the paper of Preskill and company referenced in our paper) and thought that you would need a UV completion of gravity, such as string theory, to resolve it. As we showed in the paper, you don't need to know the UV completion to resolve this puzzle: the large quantum fluctuations discussed above have such a dramatic effect on the Hawking radiation that the radiation spectrum is cut-off at high enough energies that the black hole would never go superextremal due to the emission of Hawking radiation. In describing all this, we thought it would be useful to concretely explain how this puzzle is resolved when coupling GR to the Standard Model (rather than some other QFT) and explain how such regimes are actually encountered if you let an isolated black hole evolve due to evaporation. If you read the paper, it turns out that the physics that governs Hawking radiation in such extreme black holes is quite rich and deserved to be analyzed in detail.