The instability of the inner horizon of the quantum-corrected black hole

TL;DR

This paper demonstrates that the inner horizon of a quantum-corrected black hole, modeled within loop quantum gravity, is unstable due to divergent fluxes and curvature, supporting the strong cosmic censorship hypothesis.

Contribution

It provides a stability analysis of the inner horizon in quantum-corrected black holes, revealing inevitable mass inflation and potential singularity formation.

Findings

Flux and energy density diverge near the Cauchy horizon

Mass inflation occurs regardless of the field equation

Inner horizon likely becomes a null singularity

Abstract

We analyse the stability of the inner horizon of the quantum-corrected black hole which is proposed in loop quantum gravity as the exterior of the quantum Oppenheimer-Snyder and Swiss Cheese models. It is shown that the flux and energy density of a test scalar field measured by free-falling observers are both divergent near the Cauchy horizon. By considering the generalized Dray-'t Hooft-Redmond relation which is independent of the field equation, we find that the mass inflation always happens and the scalar curvature and Kretschmann scalar are also divergent on the inner horizon. These suggest that the inner horizon is unstable and will probably turn into a null singularity. The results support the strong cosmic censorship hypothesis. However, this also implies that the quantum corrected model may not be the definitive endpoint as a regular black hole. Besides, it further proposes that it may be challenging to observe the astronomical phenomenon which depends on the existence of the inner horizon of the black hole.