Tachyonic Instability of Reissner-Nordstr\"{o}m-Melvin Black Holes in Einstein-Maxwell-Scalar Theory

TL;DR

This paper investigates how scalar field perturbations in Reissner-Nordström-Melvin black holes within Einstein-Maxwell-scalar theory lead to tachyonic instability and spontaneous scalarization influenced by magnetic fields and black hole charge.

Contribution

It demonstrates the occurrence of tachyonic instability in RNM black holes due to magnetic field effects and explores the influence of coupling sign and black hole charge.

Findings

Magnetic fields induce effective negative mass squared for scalar fields.

Tachyonic instability depends on the sign of the coupling constant.

Black hole charge affects the onset of instability.

Abstract

In the framework of Einstein-Maxwell-scalar theory, we studied scalar field perturbations of Reissner-Nordstr\"{o}m-Melvin (RNM) black holes, which describes the RN black holes immersed in a uniform magnetic field. Due to the coupling to the Maxwell term, the scalar field acquires an effective mass whose square, in the presence of the magnetic field, will become negative somewhere outside the horizon for either sign of the coupling constant $\alpha$, thus triggering the tachyonic instability and leading to spontaneous scalarization when $\alpha$ is large enough. The magnetic field has significant influences on the waveforms and the onset of the instability, which differs for different sign of $\alpha$. Effects of the black hole charge on the instability are also studied.