Dynamics of Spontaneous Black Hole Scalarization and Mergers in Einstein-Scalar-Gauss-Bonnet Gravity.

We study the dynamics of black holes in scalar Einstein-Gauss-Bonnet theories that exhibit spontaneous black hole scalarization using recently introduced methods for solving the full, nonperturbative equations of motion. For one sign of the coupling parameter, nonspinning vacuum black holes are unstable to developing scalar hair, while for the other, instability only sets in for black holes with sufficiently large spin. We study scalarization in both cases, demonstrating that there is a range of parameter space where the theory maintains hyperbolic evolution and for which the instability saturates in a scalarized black hole that is stable without symmetry assumptions. However, this parameter space range is significantly smaller than the range for which stationary scalarized black hole solutions exist. We show how different choices for the subleading behavior of the Gauss-Bonnet coupling affect the dynamics of the instability and the final state, or lack thereof. Finally, we present mergers of binary black holes and demonstrate the imprint of the scalar hair in the gravitational radiation.