Numerical simulation of the massive scalar field evolution in the Reissner-Nordstr\"{o}m black hole background

TL;DR

This paper numerically investigates how massive scalar fields evolve around Reissner-Nordström black holes, revealing how black hole and field parameters influence relaxation and decay of perturbations.

Contribution

It provides a detailed numerical analysis of scalar wave relaxation in charged black hole backgrounds, highlighting the roles of field mass, black hole mass, and charge.

Findings

Relaxation depends on the product of black hole mass and field mass, $Mm$.

For $Mm << 1$, relaxation is independent of black hole parameters.

For $Mm >> 1$, black hole parameters significantly affect relaxation.

Abstract

We studied the massive scalar wave propagation in the background of Reissner-Nordstr\"{o}m black hole by using numerical simulations. We learned that the value $Mm$ plays an important role in determining the properties of the relaxation of the perturbation. For $Mm << 1$ the relaxation process depends only on the field parameter and does not depend on the spacetime parameters. For $Mm >> 1$, the dependence of the relaxation on the black hole parameters appears. The bigger mass of the black hole, the faster the perturbation decays. The difference of the relaxation process caused by the black hole charge $Q$ has also been exhibited.