The breakdown of weak null singularities inside black holes

TL;DR

This paper proves that the weak null singularity inside black holes cannot close off the space-time, leading to a transition to a different singularity where the area-radius shrinks to zero.

Contribution

It demonstrates that the weak null singularity inside black holes necessarily breaks down and transitions into a stronger singularity, ruling out the possibility of the Cauchy horizon closing off the space-time.

Findings

Weak null singularity cannot close off the space-time.

Transition from weak null singularity to a stronger singularity.

Area-radius extends to zero at the new singularity.

Abstract

It is widely expected that generic black holes have a non-empty but weakly singular Cauchy horizon, due to mass inflation. Indeed this has been proven by the author in the spherical collapse of a charged scalar field, under decay assumptions of the field in the black exterior which are conjectured to be generic. A natural question then arises: can this weakly singular Cauchy horizon close off the space-time, or does the weak null singularity necessarily "break down", giving way to a different type of singularity? The main result of this paper is to prove that the Cauchy horizon cannot ever "close off" the space-time. As a consequence, the weak null singularity breaks down and transitions to a different singularity for which the area-radius $r$ extends to $0$.