Scalarized charged black holes with scalar mass term

TL;DR

This paper investigates scalarized charged black holes in Einstein-Maxwell-Scalar theory with a scalar mass term, revealing conditions for their existence, stability, and the influence of the mass parameter on these properties.

Contribution

It introduces the effects of a scalar mass term on scalarized charged black holes and analyzes their stability and existence conditions within this extended framework.

Findings

Scalarized black holes exist for certain parameter ranges of eta and charge.

The n=0 black hole is stable, while the n=1 black hole is unstable.

Scalarized black holes do not exist for eta .4 with the given charge.

Abstract

We study the scalarized charged black holes in the Einstein-Maxwell-Scalar (EMS) theory with scalar mass term. In this work, the scalar mass term is chosen to be $m^2_\phi=\alpha/\beta$, where $\alpha$ is a coupling parameter and $\beta$ is a mass-like parameter. It turns out that any scalarized charged black holes are not allowed for the case of $\beta \le 4.4$ with $q=0.7(M=0.5,Q=0.35)$ because this case implies the stable Reissner-Nodstr\"{o}m (RN) black holes. In the massless limit of $\beta\to \infty$, one recovers the case of the EMS theory. We note that the unstable RN black hole implies the appearance of scalarized charged black holes. The other unstable case of $\beta>4.4$ with $q=0.7$ allows us to obtain the $n=0,1,2,\cdots$ scalarized charged black holes for $\alpha(\beta)\ge \alpha_{\rm th}(\beta)$ where $\alpha_{\rm th}(\beta)$ represents the threshold of instability for the RN black hole. Furthermore, it is shown that the $n=0$ black hole is stable against radial perturbations, while the $n=1$ black hole is unstable. This stability result is independent of the mass parameter $\beta$.