Connecting Gravitational Perturbations: from Bertotti-Robinson to Extreme Reissner-Nordstrom

TL;DR

This paper investigates how perturbations in the near-horizon region of extreme Reissner-Nordstrom black holes relate to Bertotti-Robinson spacetime, establishing a gauge-dependent connection between their perturbative solutions.

Contribution

It extends the understanding of near-horizon perturbations by explicitly matching solutions in different gauges for Reissner-Nordstrom and Bertotti-Robinson spacetimes.

Findings

Identified gauge conditions for matching perturbations

Solved perturbation problems in general gauges

Established a connection between two spacetime perturbations

Abstract

We study spherically symmetric spacetime perturbations induced by a neutral scalar in the near-horizon region of extreme Reissner-Nordstrom black holes. For the unperturbed black hole, the near-horizon region is given by another exact solution of the Einstein-Maxwell equations, namely the Bertotti-Robinson spacetime. Our aim is to extend this connection beyond the background level and identify perturbations of a Bertotti-Robinson spacetime as near-horizon perturbations of an extreme Reissner-Nordstrom black hole. We explain that explicit identification of the perturbative solutions to the two different backgrounds can only work in appropriate gauges. For this reason, we first solve the two perturbation problems in the most general spherically symmetric gauges and then find the necessary gauge conditions for matching the Reissner-Nordstrom and Bertotti-Robinson perturbative solutions in the near-horizon limit.