Speed of gravitational waves and black hole hair

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.