On mass inflation and thin shells in quasi-topological gravity

TL;DR

This paper investigates null junction conditions in quasi-topological gravity, finding no null thin shells exist, which challenges the standard approach to mass inflation instability analysis in these theories.

Contribution

It demonstrates the non-existence of null thin shells in quasi-topological gravity, indicating the need for alternative methods to study inner horizon stability.

Findings

No null thin shells exist in analyzed solutions.

Mass inflation analysis via thin shells is not applicable.

Inner horizon stability remains an open problem.

Abstract

We study the null junction conditions in (re-summed) quasi-topological gravity theories, showing that no null thin shells exist within the realms of standard distributional theory for the pure gravity regular black hole solutions we have analyzed. This implies that the usual derivation of the mass inflation instability, which makes use of null thin shells, is not applicable in these theories. The problem of stability of inner horizons of regular black holes in quasi-topological gravity is hence still open and must be addressed with a more refined analysis, which does not rely on thin shells or the vacuum condition.