Late-time decay of coupled electromagnetic and gravitational perturbations outside an extremal charged black hole

TL;DR

This paper investigates the late-time decay behavior of coupled electromagnetic and gravitational perturbations around an extremal Reissner-Nordstrom black hole, extending previous scalar-field decay results to more complex perturbations.

Contribution

It provides explicit expressions for the late-time tails of gauge-invariant variables and metric and electromagnetic perturbations in the Regge-Wheeler gauge for extremal charged black holes.

Findings

Derived late-time decay tails for coupled perturbations.

Connected results to previous scalar-field decay studies.

Discussed implications for black hole stability and perturbation theory.

Abstract

In this paper we employ the results of a previous paper on the late-time decay of scalar-field perturbations of an extreme Reissner-Nordstrom black hole, in order to find the late-time decay of coupled electromagnetic and gravitational perturbations of this black hole. We explicitly write the late-time tails of Moncrief's gauge invariant variables and of the perturbations of the metric tensor and the electromagnetic field tensor in the Regge-Wheeler gauge. We discuss some of the consequences of the results and relations to previous works.