Evolving of a massless scalar field in Reissner--Nordstr\"{o}m Anti--de Sitter spacetimes

TL;DR

This paper studies how a massless scalar field evolves in Reissner--Nordstr"om Anti--de Sitter spacetime, revealing oscillatory decay, quasinormal ringing, and charge-dependent thermalization behaviors.

Contribution

It provides new insights into scalar field decay, quasinormal modes, and the influence of black hole charge in AdS spacetime, including the behavior of imaginary frequencies.

Findings

Radiative tails exhibit oscillatory exponential decay.

Approach to thermal equilibrium varies with black hole charge.

Quasinormal mode frequencies depend on multipole index.

Abstract

We investigate the evolution of a scalar field propagating in Reissner--Nordstr\"{o}m Anti--de Sitter spacetime. Due to the characteristic of spacetime geometry, the radiative tails associated with a massless scalar field propagation have an oscillatory exponential decay. The object--picture of the quasinormal ringing has also been obtained. For small charges, the approach to thermal equilibrium is faster for larger charges. However, after the black hole charge reaches a critical value, we get the opposite behavior for the imaginary frequencies of the quasinormal modes. Some possible explanations concerning the wiggle of the imaginary frequencies have been given. The picture of the quasinormal modes depending on the multipole index has also been illustrated.