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

TL;DR

This paper introduces a new singularity theorem for black holes that accommodates some chronology violations, enabling the identification of incomplete null geodesics within the black hole interior.

Contribution

It presents a novel singularity theorem that applies to black holes with chronology violation, improving upon previous theorems by locating incomplete geodesics.

Findings

Locates null incomplete geodesics inside black holes.

Allows certain forms of chronology violation in the interior.

Provides a more applicable singularity theorem for Kerr black holes.

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.