Quasinormal modes of Reissner-Nordstr\"{o}m-AdS: the approach to extremality

TL;DR

This paper investigates how the quasinormal modes of Reissner-Nordström-AdS black holes evolve as the black hole approaches extremality, revealing a transition in the damping and oscillatory behavior of the modes.

Contribution

The study introduces a numerical approach that remains stable up to extremality and analyzes the qualitative change in quasinormal modes near extremality.

Findings

Least damped mode becomes non-oscillatory at extremality

Late time signals change qualitatively near extremality

Numerical methods effectively handle extremal limit

Abstract

We consider the quasinormal spectrum of scalar and axial perturbations of the Reissner-Nordstr\"om-AdS black hole as the horizon approaches extremality. By considering a foliation of the black hole by spacelike surfaces which intersect the future horizon we implement numerical methods which are well behaved up to and including the extremal limit and which admit initial data which is nontrivial at the horizon. As extremality is approached we observe a transition whereby the least damped mode ceases to be oscillatory in time, and the late time signal changes qualitatively as a consequence.