Numerical simulation of the massive scalar field evolution in the Reissner-Nordström black hole background

Abstract

We study the massive scalar wave propagation in the background of a Reissner-Nordstr\"om black hole by using numerical simulations. We learn that the value $\mathrm{Mm}$ plays an important role in determining the properties of the relaxation of the perturbation. For $\mathrm{Mm}\ensuremath{\ll}1$ the relaxation process depends only on the field parameter and does not depend on the spacetime parameters. For $\mathrm{Mm}\ensuremath{\gg}1,$ the dependence of the relaxation on the black hole parameters appears. The bigger the 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.