Standing wave in perturbed anti-de Sitter spacetimes with a naked singularity

TL;DR

This paper studies non-dissipative standing wave solutions in perturbed Reissner-Nordström anti-de Sitter spacetimes with a naked singularity, revealing unique quasinormal mode characteristics distinct from black hole cases.

Contribution

It introduces a new class of long-lived, stationary quasinormal modes in naked singularity spacetimes, contrasting with dissipative modes in black hole spacetimes.

Findings

Standing waves have vanishing imaginary frequency parts.

Waveforms differ significantly from those of extreme RN-AdS black holes.

Naked singularities do not act as sinks or sources in gravitational systems.

Abstract

In the framework of black hole perturbation theory, this work investigates the standing wave solutions in Reissner-Nordtsr\"om (RN) anti-de Sitter (AdS) spacetimes with a naked singularity. These solutions can be viewed as a specific class of quasinormal modes exhibiting distinct characteristics. The imaginary parts of their frequencies are numerically vanishing, allowing them to persist over an extended period. Besides, these modes are predominantly stationary in terms of the evolution of spacetime waveforms. The numerical calculations are carried out employing the finite difference method, and the quasinormal frequencies extracted by the Prony method are shown to be consistent with those obtained using the matrix method. The obtained waveforms and quasinormal frequencies are shown to be drastically different from those of an extreme RN-AdS black hole. As the quasinormal modes are primarily dissipative, the non-dissipative standing waves are attributed to the nature that the singularity can neither be a sink nor a source of the gravitational system.