Roy Kerr, New Zealand physicist and pioneer in the study of the spacetime geometry of black holes, discoverer in 1963 of the Kerr metric, an exact solution of Einstein’s field equations of general relativity for a spinning black hole (generalised in 1965 to the Kerr-Newman metric, which describes black holes which are both spinning and electrically charged), has posted a provocative paper on arXiv, “Do Black Holes have Singularities?” Here is the somewhat snarky 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.
In the paper, he observes,
The consensus view for sixty years has been that all black holes have singularities. There is no direct proof of this, only the papers by Penrose outlining a proof that all Einstein spaces containing a ”trapped surface” automatically contain FALL’s. This is almost certainly true, even if the proof is marginal. It was then decreed, without proof, that these must end in actual points where the metric is singular in some unspecified way. Nobody has constructed any reason, let alone proof for this. The singularity believers need to show why it is true, not just quote the Penrose assumption.
He then argues that for all physical black holes in our universe (which will always have some angular momentum, since exact cancellation of all spin imparted by infalling objects is unphysical), there exist photon trajectories within the black hole which do not end at a singularity, and hence the theorem of Hawking and Penrose which says that the formulation of a singularity is inevitable is falsified for all but mathematically ideal black holes which cannot exist in the real universe. He concludes,
The fact that there is at least one FALL in Kerr, the axial one, which does not end in a singularity shows that there is no extant proof that singularities are inevitable. The boundedness of some affine parameters has nothing to do with singularities. The reason that nearly all relativists believe that light rays whose affine lengths are finite must end in singularities is nothing but dogma. This is the basis for all the singularity theorems of Hawking, Penrose and others and so these are at best unproven, at worst false. Even if they were true then all they would prove is that at least one light ray from the outside is asymptotic to an event horizon and is a FALL but one might have to wait for an infinite time to confirm it for accreting black holes. Proving this would make a good initial problem for a mathematically inclined doctoral student.
In conclusion, I have tried to show that whatever the Penrose and Hawking theorems prove has nothing to do with Physics breaking down and singularities appearing. Of course, it is impossible to prove that these cannot exist, but it is extremely unlikely and goes against known physics.