Horizon instability of massless scalar perturbations of an extreme Reissner-Nordstr\"om-AdS black hole

TL;DR

This paper investigates the stability of extreme Reissner-Nordström-AdS black holes under massless scalar perturbations, revealing a power-law decay of perturbations and potential instabilities at the horizon, contrasting with nonextreme cases.

Contribution

It demonstrates that extreme Reissner-Nordström-AdS black holes exhibit horizon instability with power-law decay, differing from exponential decay in nonextreme black holes, highlighting unique stability properties in AdS space.

Findings

Power-law decay of scalar perturbations on the horizon.

Blow-up occurs at lower derivative order in extreme AdS black holes.

Extreme AdS black holes tend to be more unstable than asymptotically flat black holes.

Abstract

We study the stability of extreme Reissner-Nordstr\"om-AdS black hole under massless scalar perturbations. We show that the perturbation on the horizon of the extreme Reissner-Nordstr\"om-AdS black hole experiences a power-law decay, instead of an exponential decay as observed in the nonextreme AdS black hole. On the horizon of the extreme Reissner-Nordstr\"om-AdS black hole, the blow up happens at lower order derivative of the scalar field compared with that of the extreme Reissner-Nordstr\"om black hole, which shows that extreme AdS black holes tend to instability in comparison to black holes in asymptotic flat space-times.