Dynamical charged black hole spontaneous scalarization in Anti-de Sitter spacetimes

TL;DR

This paper investigates the nonlinear dynamics of charged black hole scalarization in Anti-de Sitter spacetimes, revealing how black holes develop scalar hair under certain conditions and analyzing their phase structure.

Contribution

It provides a detailed nonlinear dynamical analysis of black hole scalarization in AdS, including the effects of charge, coupling strength, and phase transitions.

Findings

Scalarization destroys RN-AdS black holes when parameters are large.

Black hole mass initially grows exponentially during scalarization.

Phase structure analysis confirms dynamical evolution observations.

Abstract

We study the fully nonlinear dynamics of black hole spontaneous scalarizations in Einstein-Maxwell scalar theory with coupling function $f(\phi)=e^{-b\phi^{2}}$, which can transform usual Reissner-Nordstr\"om Anti-de Sitter (RN-AdS) black holes into hairy black holes. Fixing the Arnowitt-Deser-Misner mass of the system, the initial scalar perturbation will destroy the original RN-AdS black hole and turn it into a hairy black hole provided that the constant $-b$ in the coupling function and the charge of the original black hole are sufficiently large, while the cosmological constant is small enough. In the scalarization process, we observe that the black hole irreducible mass initially increases exponentially, then it approaches to and finally saturates at a finite value. Choosing stronger coupling and larger black hole charge, we find that the black hole mass exponentially grows earlier and it takes a longer time for a hairy black hole to be developed and stabilized. We further examine phase structure properties in the scalarization process and confirm the observations in the non-linear dynamical study.