In the Dark

A paper appeared on arXiv this week that has ruffled a few feathers. It’s by Roy Kerr (yes, him) and it has the abstract:

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.

arXiv:2312.00841

I don’t think this paper is as controversial as some people seem to find it. I think most of us have doubts that singularities – specifically curvature singularities – are physically real rather than manifestations of gaps in our understanding. On the other hand, this paper focusses on an interesting technical question and provides a concrete counterexample. The point is that the famous Penrose-Hawking singularity theorems don’t actually prove the existence of singularities; they prove geodesic incompleteness, i.e. that there are geodesics that can only be extended for a finite time as measured by an observer travelling along one. Geodesic incompleteness does imply the existence of some sort of boundary, often termed a trapped surface, but not necessarily that anything physical diverges there at that boundary. Though a singularity will result in geodesic incompleteness, the assertion that geodesic incompleteness necessarily implies the existence of a singularity is really just a conjecture.

For more details, read the paper. It’s technical, of course, but well written and actually not all difficult to understand.

This entry was posted on December 7, 2023 at 2:28 pm and is filed under mathematics, The Universe and Stuff with tags arXiv:2312.00841, black holes, Roy Kerr, singularity. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.