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

TL;DR

This paper investigates static black holes in scalar-Gauss-Bonnet gravity with a massive scalar field, revealing how scalar mass suppresses scalar hair, constrains coupling parameters, and affects observable properties relevant for astrophysical tests.

Contribution

It provides the first detailed numerical analysis of massive scalar clouds around black holes in Gauss-Bonnet gravity, establishing new bounds on coupling constants and exploring observational implications.

Findings

Scalar mass suppresses scalar field beyond the Compton wavelength.

New bounds on Gauss-Bonnet coupling constant for stellar mass black holes.

Analysis of black hole properties relevant for observational tests.

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 $r_h$ and the relation to the regularity condition for the scalar field. For scalar field masses $m r_h \gtrsim 10^{-1}$, this leads to a new and currently most stringent bound on sGB coupling constant $\alpha$ of $\alpha/r_h^2 \sim 10^{-1}$ 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.