Mass inflation in f(R) gravity: A conjecture on the resolution of the mass inflation singularity

TL;DR

This paper investigates mass inflation inside charged black holes in f(R) gravity, proposing that higher curvature corrections can prevent singularities and potentially resolve inner horizon instability.

Contribution

It introduces a conjecture that higher curvature corrections in f(R) gravity can keep curvature finite during mass inflation, aiding in resolving inner horizon singularities.

Findings

Mass inflation occurs near the Cauchy horizon.

Higher curvature corrections can bound the Ricci scalar.

Conjecture: General higher curvature actions may prevent singularities.

Abstract

We study gravitational collapse of a charged black hole in f(R) gravity using double-null formalism. We require cosmological stability to f(R) models; we used the Starobinsky model and the R + (1/2)cR^2 model. Charged black holes in f(R) gravity can have a new type of singularity due to higher curvature corrections, the so-called f(R)-induced singularity, although it is highly model-dependent. As the advanced time increases, the internal structure will approach the Cauchy horizon, which may not be an inner apparent horizon. There is mass inflation as one approaches the Cauchy horizon and hence the Cauchy horizon may be a curvature singularity with nonzero area. However, the Ricci scalar is finite for an out-going null observer. This can be integrated as follows: Cosmologically stable higher curvature corrections of the Ricci scalar made it bounded even in the presence of mass inflation. Finally, we conjecture that if there is a general action including general higher curvature corrections with cosmological stability, then the corrections can make all curvature components finite even in the presence of mass inflation. This might help us to resolve the problem of inner horizon instability of regular black hole models.