Scalar field evolution in Gauss-Bonnet black holes

TL;DR

This paper analyzes scalar field perturbations in various Gauss-Bonnet black hole spacetimes, revealing how the evolution depends on the cosmological constant and coupling, with significant corrections to quasinormal modes and analytical solutions in certain limits.

Contribution

It provides a comprehensive analysis of scalar perturbations in Gauss-Bonnet black holes, including late-time tails, quasinormal modes, and analytical expressions for specific parameter limits.

Findings

Late-time tails are power-law or exponential depending on spacetime.

Gauss-Bonnet coupling significantly affects quasinormal modes.

Analytical expressions are derived for near extremal cosmological constants.

Abstract

It is presented a thorough analysis of scalar perturbations in the background of Gauss-Bonnet, Gauss-Bonnet-de Sitter and Gauss-Bonnet-anti-de Sitter black hole spacetimes. The perturbations are considered both in frequency and time domain. The dependence of the scalar field evolution on the values of the cosmological constant $\Lambda$ and the Gauss-Bonnet coupling $\alpha$ is investigated. For Gauss-Bonnet and Gauss-Bonnet-de Sitter black holes, at asymptotically late times either power-law or exponential tails dominate, while for Gauss-Bonnet-anti-de Sitter black hole, the quasinormal modes govern the scalar field decay at all times. The power-law tails at asymptotically late times for odd-dimensional Gauss-Bonnet black holes does not depend on $\alpha$, even though the black hole metric contains $\alpha$ as a new parameter. The corrections to quasinormal spectrum due to Gauss-Bonnet coupling is not small and should not be neglected. For the limit of near extremal value of the (positive) cosmological constant and pure de Sitter and anti-de Sitter modes in Gauss-Bonnet gravity we have found analytical expressions.