Black holes and binary mergers in scalar Gauss-Bonnet gravity: Scalar field dynamics

We study the nonlinear dynamics of black holes that carry scalar hair and binaries composed of such black holes. The scalar hair is due to a linear or exponential coupling between the scalar and the Gauss-Bonnet invariant. We work perturbatively in the coupling constant of that interaction but nonperturbatively in the fields. We first consider the dynamical formation of hair for isolated black holes of arbitrary spin and determine the final state. This also allows us to compute for the first time the scalar quasinormal modes of rotating black holes in the presence of this coupling. We then study the evolution of nonspinning black hole binaries with various mass ratios and produce the first scalar waveform for a coalescence. An estimate of the energy loss in scalar radiation and the effect this has on orbital dynamics and the phase of gravitational waves (GWs) (entering at quadratic order in the coupling) shows that GW detections can set the most stringent constraint to date on theories that exhibit a coupling between a scalar field and the Gauss-Bonnet invariant.