Time evolutions of scalar field perturbation in Schwarzschild de-Sitter black hole from Einstein-scalar–Gauss–Bonnet theory

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