A new singularity theorem for black holes which allows chronology violation in the interior

Abstract

The interior of the Kerr solution is singular and achronological. The classic singularity theorem by Hawking and Penrose relies on chronology, and thus does not apply to the Kerr solution. An improvement of their theorem by Kriele partially removes the requirement of chronology. However, both of these singularity theorems fail to give any information on the type or location of the incomplete geodesics. Here, using recent results of Minguzzi, we prove a new singularity theorem, specifically designed to apply to black holes, which enables locating null incomplete geodesics within the black hole interior, all the while allowing certain forms of chronology violation in the interior.

A critical appraisal of the singularity theorems

“…Finally, as an aside remark, to this day there is no theorem available that can ‘predict’ the singularity in the (analytically maximally extended) Kerr black hole despite very interesting and clever recent attempts [60–62]. Will there ever be one?…”

A critical appraisal of the singularity theorems

“…Finally, as an aside remark, to this day there is no theorem available that can "predict" the singularity in the (analitycally maximally extended) Kerr black hole despite very interesting and clever recent attempts [31,36,37]. Will there ever be one?…”