Stability analysis on charged black hole with non-linear complex scalar

TL;DR

This paper investigates the stability and phase transition properties of charged black holes with non-linear complex scalar fields, demonstrating that scalarization can occur via first order phase transitions and analyzing their stability and implications for Penrose inequalities.

Contribution

It proves that scalarization cannot be a continuous phase transition and shows that first order phase transitions can spontaneously scalarize RN black holes, with stability analysis and implications for Penrose conjectures.

Findings

Scalarization cannot result from continuous phase transition.

RN black holes can undergo first order scalarization.

Scalarized black holes are thermodynamically and kinetically stable.

Abstract

It has been shown recently that the charged black hole can be scalarized if Maxwell field minimally couples with a complex scalar which has nonnegative nonlinear potential. We firstly prove that such scalarization cannot be a result of continuous phase transition for general scalar potential. Furthermore, we numerically find that it is possible that the RN black hole will be scalarized by a first order phase transition spontaneously and extreme RN black hole is not stable in micro-canonical ensemble. In addition, considering a massless scalar perturbation, we compute the quasi-normal modes of the scalarized charged black hole and the results imply that the spontaneously scalarized charged black hole is not only favored in thermodynamics but also is kinetically stable against scalar perturbation at linear level. Our numerical results also definitely gives negative answer to Penrose-Gibbons conjecture and two new versions of Penrose inequality in charged case are suggested.