Hawking radiation may smooth black hole singularities

[atyy]

Bizarre Hawking radiation may smooth the jagged hearts of black holes
Adrian Cho
https://www.science.org/content/art...adiation-may-smooth-jagged-hearts-black-holes

Radiating black holes in general relativity need not be singular
Francesco Di Filippo
https://arxiv.org/abs/2510.20649

Can black holes evaporate past extremality?[/HEADING]
Samuel E. Gralla
https://arxiv.org/abs/2510.18839

 

[PeterDonis]

All of this is of course highly speculative, since we have no evidence in the relevant physical regime and aren't likely to get any any time soon.

 

[PeterDonis]

Radiating black holes in general relativity need not be singular
Francesco Di Filippo
https://arxiv.org/abs/2510.20649

Can black holes evaporate past extremality?[/HEADING]
Samuel E. Gralla
https://arxiv.org/abs/2510.18839

Both of these seem like they're more or less rediscovering the Bardeen black hole (a misnomer as the solution actually contains no true event horizon, only apparent horizons), just with charge or angular momentum added. We've had a number of previous PF threads that discuss the Bardeen black hole.

 

[Demystifier]

Does it shed some light on the information paradox?

 

[PeterDonis]

Does it shad some light on the information paradox?

In a Bardeen black hole solution, there is no information paradox because there is no true event horizon anywhere. The causal structure of the spacetime is the same, qualitatively, as flat Minkowski spacetime, and there is no issue at all with maintaining quantum unitarity. Similar remarks seem to me to apply to the nonsingular solutions presented in these papers.

 

[Demystifier]

In a Bardeen black hole solution, there is no information paradox because there is no true event horizon anywhere. The causal structure of the spacetime is the same, qualitatively, as flat Minkowski spacetime, and there is no issue at all with maintaining quantum unitarity. Similar remarks seem to me to apply to the nonsingular solutions presented in these papers.

My confusion stems from the following. The Bardeen metric significantly deviates from the Schwarzschild only for small $r$, close to $r=0$. And yet, global properties significantly deviate from the Schwarzschild even for larger $r$, e.g. close to $r=2M$. How to understand that? What do I miss?

 

[PeterDonis]

The Bardeen metric significantly deviates from the Schwarzschild only for small $r$, close to $r=0$.

If you mean in the supposed "vacuum" region, that's kinda sorta true--the "hole" becomes effectively de Sitter only at very small $r$.

However, the full solution includes two very important non vacuum regions. One is just the formation of the "hole" by collapse of matter (or radiation--in the simplest model, it's just an ingoing Vaidya metric region); the other is the evaporation of the "hole" (in the simplest model, this is just an outgoing Vaidya metric region). The presence of the latter region is crucial for the global properties.

There is also the point that, even if the "vacuum" region is only de Sitter at very small $r$, that's precisely the region where the global causal structure has to change to avoid the formation of a singularity. And of course de Sitter is nonsingular everywhere, so any region that's de Sitter must also be nonsingular.

Physically, the de Sitter region is what enables the infalling stress-energy that forms the "hole" to "bounce", so to speak, and "escape" back out, while keeping the overall causal structure the same as Minkowski spacetime. The "escape" then requires the outgoing Vaidya region (modeled that way because it's expected that the vast majority of the stress-energy will escape as light).

 

[Demystifier]

The "escape" then requires the outgoing Vaidya region (modeled that way because it's expected that the vast majority of the stress-energy will escape as light).

Is this something like a white hole?

 

[PeterDonis]

Is this something like a white hole?

No, because there's no white hole horizon, any more than there's a black hole horizon. It's just outgoing radiation. The portion of the outgoing Vaidya spacetime that's used is outside the white hole horizon of that spacetime.

 

[javisot]

In a Bardeen black hole solution, there is no information paradox because there is no true event horizon anywhere.

Could you provide a reference on this? I'm not aware of any that demonstrates the absence of an information paradox in Bardeen black holes.

I recall physicist J. Edelstein saying that the information paradox also exists in regular black holes; there is still a black hole and trapped information despite the absence of a singularity and the apparent event horizon.

 

[PeterDonis]

Could you provide a reference on this? I'm not aware of any that demonstrates the absence of an information paradox in Bardeen black holes.

The causal structure of the Bardeen black hole is the same as that of Minkowski spacetime. AFAIK it's well understood in the QFT community that any spacetime with that causal structure has no "information paradox", for the same reason standard QFT in Minkowski spacetime does not.

I recall physicist J. Edelstein saying that the information paradox also exists in regular black holes; there is still a black hole and trapped information despite the absence of a singularity and the apparent event horizon.

Can you give a reference for this? The term "regular black hole" is ambiguous. I would need to know more precisely what he means by it.

 

[javisot]

Can you give a reference for this? The term "regular black hole" is ambiguous. I would need to know more precisely what he means by it.

https://arxiv.org/abs/2412.02742
"Dynamical formation of regular black holes", Pablo Bueno (Spain).

In this case, they construct the black hole using a tower of infinite corrections. Regular black holes are those that have neither a real horizon nor a singularity; Bardeen's black hole is a regular black hole, the first known example of a regular black hole.

*I'm adding more references about regular black holes in case you're interested:

https://arxiv.org/abs/2303.11696
https://arxiv.org/abs/2205.13556
https://arxiv.org/abs/2403.04827

 

[PeterDonis]

using a tower of infinite corrections

...to the Einstein-Hilbert action, i.e., by modifying GR. But you don't need to do that to get a "regular black hole" such as the Bardeen black hole--that solution is a solution to the standard GR Einstein Field Equation.

Regular black holes are those that have neither a real horizon nor a singularity

Meaning, they're not actually black holes. The standard definition of the term "black hole" (see, for example, Wald, Chapter 12) is a region of spacetime that is not in the causal past of future null infinity. In the spacetimes you're referring to, such as the Bardeen black hole, there is no such region; the entire spacetime is in the causal past of future null infinity. That is what I meant before when I said that these spacetimes have the same causal structure as Minkowski spacetime. And for any such spacetime, AFAIK it is well established in the QFT literature that there is no issue at all with constructing a unitary QFT. So any claim that there can still be an "information paradox" in such a spacetime seems obviously wrong to me.

It's typical, of course, for misnomers like "regular black hole" to become entrenched in the scientific literature. But if in this case the misnomer is leading physicists to conclude from the term "black hole" that there is still an issue with quantum unitarity in these spacetimes, then I think the misnomer is harmful.

That said, I note that the reference you gave does not appear to discuss the information paradox issue at all. If there are indeed physicists who are claiming that there is still an information paradox in "regular black hole" spacetimes, I need to see specific references from those physicists that make and defend that claim--because, as I said above, it seems obviously wrong to me.

 

[javisot]

In a Bardeen black hole solution, there is no information paradox because there is no true event horizon anywhere.

The causal structure of the Bardeen black hole is the same as that of Minkowski spacetime. AFAIK it's well understood in the QFT community that anyspacetime with that causal structure has no "information paradox", for the same reason standard QFT in Minkowski spacetime does not.

Can I ask you for references on this again?

 

[PeterDonis]

Can I ask you for references on this again?

I don't know that I'll be able to find a reference in the QFT literature that specifically says the thing you appear to be looking for--because it's considered so obvious that nobody bothers to explicitly point it out. Just as for Minkowski spacetime--nobody bothers to prove that you can construct a unitary QFT on Minkowski spacetime and state that in a paper, because it's been done countless times for decades and everyone in the field knows it.

Perhaps it's worth expanding at a heuristic level on why it's obvious that you can construct a unitary QFT on any spacetime with the same causal structure as Minkowski spacetime. "Causal structure" here means: where is it possible for inextendible causal curves to come from? And to go? In Minkowski spacetime, they have to come from either past timelike infinity or past null infinity, and they have to go to either future timelike infinity or future null infinity. There are no other places for them to come from or to go. And those places correspond, in QFT terms, to "where massive/massless particles come from at the start of the experiment" and "where massive/massless particles go to at the end of the experiment". In other words, with this causal structure, it's impossible for anything to get "lost" somewhere during the experiment--everything that goes in has to come out. And that's another way of saying quantum unitarity is obviously satisfied and there is no information paradox.

The reason there is an information paradox for, e.g., a spacetime with a Schwarzschild black hole formed by gravitational collapse, is that, while everything still has to come from past timelike or null infinity, there is now another place where things can go that isn't future timelike or null infinity--things can go into the black hole. In other words, there are inextendible causal curves that come from past timelike or null infinity, go into the black hole, and never come out. And even if the hole ends up evaporating away due to Hawking radiation, that is still true--there are still inextendible causal curves that don't come out in the Hawking radiation. So the presence of the black hole region at all creates a problem with constructing a unitary QFT, because everything we think we know about GR and quantum gravity says that information about the things that fell into the hole gets lost--it isn't contained in the Hawking radiation that comes out, since that radiation is supposed to be thermal radiation, with no correlations to anything that fell in. That is what creates the "information paradox"--heuristically, information can get lost inside the black hole region and never come out again, and that violates quantum unitarity.

But if there is no black hole region--with the strict Wald definition of "black hole" as a region not in the causal past of future infinity--then there's no place for information to get lost; there are no causal curves that go in and don't come out. So there can't be a problem with quantum unitarity.

 

[javisot]

But if there is no black hole region--with the strict Wald definition of "black hole" as a region not in the causal past of future infinity--then there's no place for information to get lost; there are no causal curves that go in and don't come out. So there can't be a problem with quantum unitarity.

The Bardeen black hole also evaporates via Hawking radiation, but whether the process is unitary seems to depend on adding backreaction, at least in the case of regular black holes (Bardeen-like model) in 2D dilaton gravity. https://arxiv.org/abs/2503.03191

 

[PeterDonis]

The Bardeen black hole also evaporates via Hawking radiation

For some values of "Hawking radiation", yes.

whether the process is unitary seems to depend on adding backreaction, at least in the case of regular black holes (Bardeen-like model) in 2D dilaton gravity. https://arxiv.org/abs/2503.03191

Physically speaking, "backreaction" isn't something that needs to be "added". It just means "the mass of the thing in the center decreases as radiation escapes". Which is going to happen in any model that satisfies the Einstein Field Equation and quantum unitarity, since any such model will obey local energy conservation.

What the paper means by "including backreaction" is, as the end of that same sentence in the abstract implies, the fully coupled equations can't be solved analytically so they have to be solved numerically. In the past, when the sort of computing power that's commonplace now wasn't available (which is an understatement ), people would write down approximate equations that could be solved analytically, and then come up with some kind of argument that their solutions were close enough to the actual solutions of the actual correct equations to be useful. "Backreaction" is basically acknowledging that for this particular problem, that wasn't the case--the approximate equations you write down that you can solve analytically simply don't tell you what you need to know, because they had to leave out the part where the energy carried away by the Hawking radiation reduces the mass of what's left behind--because including that part would make the equations not solvable analytically.