Scalarized charged black holes in the Einstein-Maxwell-Scalar theory with two U(1) fields

TL;DR

This paper studies scalarized charged black holes with two U(1) fields in Einstein-Maxwell-Scalar theory, classifies them by excitation level, and analyzes their stability, finding the fundamental black hole stable and excited states unstable.

Contribution

It introduces a classification of scalarized black holes by excitation number and analyzes their stability within the Einstein-Maxwell-Scalar framework with two U(1) fields.

Findings

The fundamental black hole (n=0) is stable against scalar perturbations.

Excited black holes (n=1,2) are unstable.

The n=0 black hole acts as an endpoint of the Reissner-Nordström black hole.

Abstract

We investigate scalarized charged black holes in the Einstein-Maxwell-Scalar theory with two U(1) fields inspired by the $N=4$ supergravity. From the onset of the spontaneous scalarization (tachyonic instability of Reissner-Nordstr\"{o}m black hole), these black holes are classified by the number of $n=0,1,2,\cdots$, where $n=0$ is called the fundamental black hole and $n=1,2,\cdots$ denote the $n$-excited black holes. Adopting radial perturbations, we show that the $n=0$ black hole is stable against the $s(l=0)$-mode scalar perturbation, whereas the $n=1,2$ excited black holes are unstable. This implies that the $n=0$ black hole is considered as an endpoint of the Reissner-Nordstr\"{o}m black hole.