Relaxation rate of RNdS black hole

TL;DR

This paper studies how the relaxation rate of RNdS black holes, perturbed by scalar fields, varies with the cosmological constant and charge across different dimensions, revealing dimension-dependent behaviors.

Contribution

It provides a detailed analysis of the relaxation rates of RNdS black holes in various dimensions, highlighting the influence of the cosmological constant and charge on these rates.

Findings

Relaxation rate increases with cosmological constant in all dimensions.

Critical charge for maximum relaxation rate decreases with decreasing cosmological constant in 4D.

Higher dimensions show different trends in critical charge behavior.

Abstract

We investigate the relaxation rate of the RNdS black hole perturbed by neutral massless scalar field in the eikonal limit. We find that the fastest relaxation rate of the composed system increases with the cosmological constant for all spacetime dimensions. We also find that, when the cosmological constant decreases from maximum value to zero, the corresponding critical charge of the four-dimensional RNdS black hole maximizing the relaxation rate of the composed system gradually decreases monotonically to $\bar{Q}=0.726$. However, for the higher dimensional systems, this is not the case and the critical charges decrease from maximum to zero.