Time evolutions of scalar field perturbation in Schwarzschild de-Sitter black hole from sEGB theory

Abstract

The scalar free black hole could be unstable against the scalar field perturbation when it is coupled to Gauss-Bonnet (GB) invariant in a special form. It is known that the tachyonic instability in this scenario is triggered by the strong enough GB coupling. In this paper, we focus on the time domain analysis of massive scalar field perturbation around the Schwarzschild de-Sitter (SdS) black hole in scalar-Einstein-Gauss-Bonnet (sEGB) gravity. By analyzing the scalar field propagation, we find that the scalar field will finally grow up when the GB coupling is large enough. This could lead to the instability of background black hole. Furthermore, we demonstrate how the mass of the scalar field and the GB coupling strength affect the onset of tachyonic instability.