Do Black Holes have Singularities?

[fresh_42]

TL;DR

Do Black Holes have Singularities?
paper by Roy Kerr on arxiv.org

Do Black Holes have Singularities?​

"There is no proof that black holes contain singularities when they are generated by real physical bodies. Roger Penrose claimed sixty years ago that trapped surfaces inevitably lead to light rays of finite affine length (FALL's). Penrose and Stephen Hawking then asserted that these must end in actual singularities. When they could not prove this they decreed it to be self evident. It is shown that there are counterexamples through every point in the Kerr metric. These are asymptotic to at least one event horizon and do not end in singularities."

https://arxiv.org/abs/2312.00841

The pop science world advertises as "Hawking and Penrose were wrong"

Kerr writes, referring to Penrose and Hawking: “It has not been proven that a singularity is inevitable when an event horizon forms around a collapsing star.” Hawking and Penrose's point is that light rays within a black hole are finite - they would then have to end in a singularity. However, Kerr now says that Hawking and Penrose drew wrong conclusions. “This is perhaps the most surprising development in theoretical physics that I have seen in a decade,” writes theoretical physicist Sabine Hossenfelder of the Munich Center for Mathematical Philosophy on X. In a video she further explains: “It seems that Kerr’s argument is almost certainly mathematically correct. And it’s not even a particularly difficult argument, to the shame of many theoretical physicists, myself included.”
https://www.merkur.de/wissen/astrop...eue-studie-mathematiker-kerr-zr-92738471.html

My question to everyone who can actually rate the article is: What can we really expect?

Edit: Quotation marks added to the text before the link.

 

[PeterDonis]

We had a thread on this paper not long ago:

https://www.physicsforums.com/threads/kerr-disputes-singularities-in-kerr-black-holes.1057975/

 

[PeterDonis]

There is no proof that black holes contain singularities when they are generated by real physical bodies.

This is actually not what Kerr's paper says. Kerr's paper says that there are lightlike FALLs in the maximally extended Kerr metric that do not end on either of the ring singularities. That is of course correct (since it's a proven mathematical theorem). But it has nothing to do with the question of what the collapse of an actual physical body will end up producing. That question depends on many factors, some of which we don't currently understand (such as whether or not quantum fields end up changing the equation of state so that it violates the energy conditions that are part of the premises of the singularity theorems, and therefore can produce geometries from collapse that not only have no singularities, but also have no event horizons, such as the Bardeen black hole, which I mention in the previous thread I linked to).

(Also, as I pointed out in that previous thread, Kerr appears to be using the wrong definition of the term "singularity", and as a result the claims he says he is rebutting in the paper, as far as I can tell, are claims that nobody in the GR community actually makes.)

 

[PeterDonis]

Penrose and Stephen Hawking then asserted that these must end in actual singularities.

As I noted in my previous post (referring to the previous thread I linked to), you have to be very careful about what "singularity" actually means here. The Penrose and Hawking theorems say there must be inextendible geodesics in any spacetime that satisfies the energy conditions and has a trapped surface; and the actual definition of the term "singularity" is that inextendible geodesics are present. They do not say all of those inextendible geodesics must end on a "singularity" in the sense of a locus where curvature invariants increase without bound (which is the chief characteristic that picks out the ring singularities in maximally extended Kerr spacetime). As far as I can tell, Kerr fails to make this critical distinction.

 

[PeterDonis]

There is good background information in this old thread from Chris Hillman:

https://www.physicsforums.com/threads/roy-kerr-on-the-kerr-vacuum.173650/

 

[fresh_42]

My bad. Both statements you answered were actually a quotation of Kerr. I inserted the abstract on the title page on arxiv.org. I thought the link would do, but I should have used "" at least, sorry.

Nevertheless, it resulted in an interesting experiment. You claim that Kerr doesn't say what Kerr said, just by the fact that you thought it was me.

 

[pines-demon]

TL;DR Summary: Do Black Holes have Singularities?
paper by Roy Kerr on arxiv.org

The pop science world advertises as "Hawking and Penrose were wrong"

Could you provide the pop science article too?

 

[fresh_42]

Could you provide the pop science article too?

It is in the spoiler below the quotation, but it was a German newspaper found in my fb feed.
https://www.merkur.de/wissen/astrop...eue-studie-mathematiker-kerr-zr-92738471.html

 

[PeterDonis]

You claim that Kerr doesn't say what Kerr said, just by the fact that you thought it was me.

To clarify, I understand that Kerr makes the claims in the paper that you stated. I just think he misstates them. I go into that in more detail in the previous thread I linked to.

 

[fresh_42]

To clarify, I understand that Kerr makes the claims in the paper that you stated. I just think he misstates them. I go into that in more detail in the previous thread I linked to.

... which I have read. I just wanted to say that "my" quotations were Kerr's.

 

[pervect]

Somewhat but not totally related to the thread.

Relatively small modifications of GR (so small that current experiments can't test for them) can result in a "big bounce" rather than a singularity for realistic collapse.

See for instance https://arxiv.org/abs/1111.4595, which Google reports as having 182 citations. The modification to GR is the Einstein-Cartan-Sciama-Kibble theory (also known as Einstein-Cartan theory), which has the advantage of much better handling spin 1/2 particles in the theory. See also the wiki, https://en.wikipedia.org/wiki/Einstein–Cartan_theory.

 

[martinbn]

Somewhat but not totally related to the thread.

Relatively small modifications of GR (so small that current experiments can't test for them) can result in a "big bounce" rather than a singularity for realistic collapse.

See for instance https://arxiv.org/abs/1111.4595, which Google reports as having 182 citations. The modification to GR is the Einstein-Cartan-Sciama-Kibble theory (also known as Einstein-Cartan theory), which has the advantage of much better handling spin 1/2 particles in the theory. See also the wiki, https://en.wikipedia.org/wiki/Einstein–Cartan_theory.

The paper doesn't treat realistic collapse, or am I missing something? I looked at it and it seems to work only with homogenous and isotropic cosmological models.

 

[PeterDonis]

The paper doesn't treat realistic collapse, or am I missing something? I looked at it and it seems to work only with homogenous and isotropic cosmological models.

The spacetime region occupied by matter in a collapse to a black hole is the time reverse of those models (for example, in the original Oppenheimer-Snyder 1939 paper). So the "bounce" works the same way in both cases.

 

[martinbn]

The spacetime region occupied by matter in a collapse to a black hole is the time reverse of those models (for example, in the original Oppenheimer-Snyder 1939 paper). So the "bounce" works the same way in both cases.

That's a good point but it is still isotropic, which is not generic.

 

[PeterDonis]

it is still isotropic, which is not generic

Yes, it's an idealization, because you have to use such idealizations if you want to work with a closed form solution. "Generic" collapse and "bounce" can only be dealt with numerically; there are no known closed form solutions.

 

[martinbn]

Yes, it's an idealization, because you have to use such idealizations if you want to work with a closed form solution. "Generic" collapse and "bounce" can only be dealt with numerically; there are no known closed form solutions.

But one doesn't have to work with a closed form solution. Like the Penrose, Hawking, and others' singularity theorems. Can singularities be avoided more generally in EC?

 

[PeterDonis]

Can singularities be avoided more generally in EC?

I don't think there are general "no singularity theorems" in EC to mirror the singularity theorems in standard GR.

 

[PeterDonis]

Moderator's note: Thread level changed to "A" based on the nature of the subject matter, which requires a graduate level background.

 

[PeterDonis]

We can consider the gravitational force of a neutron star on an asteroid rotating around it.

Not for this purpose. Your analysis, to the extent it's even valid, is Newtonian, but the question under discussion here is a GR question in a domain where Newtonian physics is already known to be wrong.

 

[pervect]

The paper doesn't treat realistic collapse, or am I missing something? I looked at it and it seems to work only with homogenous and isotropic cosmological models.

Realistic collapse has even more issues to consider. Hamilton, et al, in their work on realistic collapse, has followed the lead of Penrose in suggesting "mass inflation" and "relativistic counter-streaming at the horizon". See for instance https://arxiv.org/abs/0811.1926 (google reports 74 citations).

If you fall into a real astronomical black hole (choosing a supermassive black hole, to make sure that the tidal forces don't get you first), then you will probably meet your fate not at a central singularity, but rather in the exponentially growing, relativistic counter-streaming instability at the inner horizon first pointed out by Poisson & Israel (1990), who called it mass inflation.

Hamilton et al have some ideas on applying these ideas to rotating black holes, but the citation count for the associated papers is lower. See for instance https://journals.aps.org/prd/abstract/10.1103/PhysRevD.84.124055.

There are some other interesting ideas for black hole collapse as well, such as the BKL singularity, which is a chaotic solution. See for instance https://en.wikipedia.org/wiki/BKL_singularity. I first ran across the BKL singularity in Kip Thorne's popular book, "Black Holes and Time Warps", where Thorne mentioned he favored it (at the time the book was written) as a candidate for realistic collapse, for whatever that's worth to you. The wiki article has a citation for the original, Russian paper, and an English translation - I'm not sure how widely they are cited in the literature.

There is some interesting history mentioned in the Wiki article (simlar to what I recall reading in Thorne's popularization).

One of the principal problems studied by the Landau group (to which BKL belong) was whether relativistic cosmological models necessarily contain a time singularity or whether the time singularity is an artifact of the assumptions used to simplify these models.

An example of such an assumption would be perfectly spherical initial condition characteristic of the Kerr solution, as opposed to initial conditions that were not perfectly spherical.

A short summary of the history - The Lanadau group searched for and failed to find general solutions which had a singularity. When Penrose's focusing theorem came out, they looked harder and found the aforementioned chaotic BKL solution, with the aid of some conjectures.

Both of the above (mass inflation and the BKL singularity) are within classical GR, unlike the Einstein-Cartan theories I mentioned previously.

 

[PeterDonis]

perfectly spherical initial condition characteristic of the Kerr solution

I think you mean the Schwarzschild solution. The Kerr solution (rotating hole) is only axisymmetric, not spherically symmetric.