The formation of a weak null singularity in the interior of generic rotating black holes

TL;DR

This paper proves that a weak null singularity forms inside generic rotating black holes, where the spacetime metric remains continuous but not Lipschitz, based on stability and approximation of Teukolsky fields.

Contribution

It demonstrates the formation of a weak null singularity in rotating black holes using stability analysis and Teukolsky field approximations.

Findings

Weak null singularity forms inside rotating black holes

Spacetime metric is continuous but not Lipschitz extendible

Dynamical Teukolsky fields can be approximated by linear fields

Abstract

Given a characteristic initial value problem with smooth data representing a dynamical event horizon settling down to that of Kerr in the subextremal, strictly rotating range with suitable upper and lower bounds, we prove that a weak null singularity forms, across which the spacetime metric is continuously extendible but not Lipschitz extendible. The bulk of the proof is a stability argument showing that a dynamical Teukolsky field can be approximated by a linear Teukolsky field, whose linear instability was proved in previous works.