Massive scalar clouds and black hole spacetimes in Gauss-Bonnet gravity

Abstract

We study static black holes in scalar-Gauss-Bonnet (sGB) gravity with a massive scalar field as an example of higher curvature gravity. The scalar mass introduces an additional scale and leads to a strong suppression of the scalar field beyond its Compton wavelength. We numerically compute sGB black hole spacetimes and scalar configurations and also compare with perturbative results for small couplings, where we focus on a dilatonic coupling function. We analyze the constraints on the parameters from requiring the curvature singularity to be located inside the black hole horizon rh and the relation to the regularity condition for the scalar field. For scalar field masses mrh ≳ 10−1, this leads to a new and currently most stringent bound on sGB coupling constant α of α/rh2 ∼ 10−1 in the context of stellar mass black holes. Lastly, we look at several properties of the black hole configurations relevant for further work on observational consequences, including the scalar monopole charge, Arnowitt–Deser–Misner mass, curvature invariants and the frequencies of the innermost stable circular orbit and light ring.