Spontaneous scalarization and dynamical evolution of black holes in scalar-Gauss-Bonnet gravity

Abstract We investigate the nonlinear dynamics of black holes in an Einstein-scalar-Gauss-Bonnet (EsGB) gravity theory where a real scalar field couples to both the Gauss-Bonnet invariant and the Ricci scalar through a higher-order coupling function. Starting from both bald and hairy static solutions, we perform full numerical simulations in Painlevé–Gullstrand-like coordinates to follow the time evolution triggered by localized scalar field pulses. We identify the scalarization threshold of the static solutions and uncover four distinct dynamical channels: stable Schwarzschild black holes resisting scalar growth; spontaneous scalarization of Schwarzschild black holes into stable hairy configurations; transitions between metastable and stable hairy states; and complete descalarization of metastable or weakly perturbed hairy black holes back to the Schwarzschild phase. Energy redistribution is quantified using the Misner–Sharp mass, which reveals horizon mass growth and energy transport. The effective stress-energy tensor violates the null convergence condition during scalarization, indicating regions of negative effective energy that support hair formation. Our results demonstrate that scalarized black holes emerge naturally as nonlinear end states of evolution in EsGB gravity, and they highlight the rich phase-space structure and dynamical behavior beyond general relativity.