Speed of gravitational waves and black hole hair

TL;DR

This paper examines whether modified gravity theories consistent with gravitational wave speed constraints allow black hole hair, finding that most do not, thus narrowing the scope of viable theories.

Contribution

It provides a comprehensive analysis of black hole hair in scalar-tensor and other modified gravity theories respecting the gravitational wave speed constraint.

Findings

Theories with $c_T=1$ generally do not allow black hole hair.

Most scalar-tensor theories respecting $c_T=1$ have negligible or no hair.

Comments on vector-tensor and bimetric theories regarding black hole hair.

Abstract

The recent detection of GRB 170817A and GW170817 constrains the speed of gravity waves $c_T$ to be that of light, which severely restricts the landscape of modified gravity theories that impact the cosmological evolution of the universe. In this work, we investigate the presence of black hole hair in the remaining viable cosmological theories of modified gravity that respect the constraint $c_T=1$. We focus mainly on scalar-tensor theories of gravity, analyzing static, asymptotically flat black holes in Horndeski, Beyond Horndeski, Einstein-Scalar-Gauss-Bonnet, and Chern-Simons theories. We find that in all of the cases considered here, theories that respect $c_T=1$ do not allow for hair, or have negligible hair. We further comment on vector-tensor theories including Einstein Yang-Mills, Einstein-Aether, and Generalised Proca theories, as well as bimetric theories.