Decay of massive scalar field in a black hole background immersed in magnetic field

TL;DR

This paper investigates how a magnetic field affects the decay of massive scalar fields around black holes by analyzing quasinormal modes in the Ernst spacetime, revealing that magnetic fields can slow decay rates.

Contribution

It introduces the effect of magnetic fields on scalar field decay in black hole backgrounds and computes the resulting quasinormal modes in the Ernst spacetime.

Findings

Increasing magnetic field strength reduces the damping rate of scalar perturbations.

Effective mass of scalar field increases with magnetic field, affecting decay properties.

Decay rates can approach zero, indicating long-lived modes.

Abstract

We evaluate quasinormal modes of massive scalar field of the Ernst spacetime, an exact solution of the Einstein-Maxwell equations describing a black hole immersed in uniform magnetic field $B$. It is known that the quasinormal spectrum for massive scalar field in the vicinity of the magnetized black holes acquires an effective mass $\mu_{eff}= \sqrt{4B^2 m^2+\mu^2}$, where $m$ is the azimuthal number and $\mu$ is the mass of scalar field. The numerical result shows that increasing of the field effective mass and the magnetic field $B$ gives rise to decreasing of the imaginary part of the quasinormal modes until reaching the vanishing damping rate.