Stability of self-dual black holes

TL;DR

This paper investigates the stability of Cauchy horizons in two self-dual black hole models inspired by Loop Quantum Gravity, revealing conditions under which these horizons remain stable or are protected by symmetries.

Contribution

It provides a comparative analysis of the stability of Cauchy horizons in two self-dual black hole solutions, highlighting the role of symmetries and parameters in horizon stability.

Findings

Cauchy horizon stability depends on black hole size and the polymeric parameter P.

Small black holes with the first metric have stable Cauchy horizons if P is small.

The second metric's symmetry ensures horizon stability for all P values.

Abstract

We study the stability properties of the Cauchy horizon for two different self-dual black hole solutions obtained in a model inspired by Loop Quantum Gravity. The self-dual spacetimes depend on a free dimensionless parameter called a polymeric parameter P. For the first metric the Cauchy horizon is stable for supermassive black holes only if this parameter is sufficiently small. For small black holes, however the stability is easily implemented. The second metric analyzed is not only self-dual but also "form-invariant" under the transformation r -> r*^2/r and r* = 2 m P. We find that this symmetry protects the Cauchy horizon for any value of the polymeric parameter.