This research proposal explores the nonlinear stability of Gauss-Bonnet scalarized black holes, a mechanism to bypass classical no-hair theorems. It combines second-order perturbation theory and numerical relativity to address thresholds for instability, effects of nonlinear mode couplings, and the fate of nonlinear perturbations.
Key findings
Spontaneous scalarization allows black holes to develop scalar hair, challenging no-hair theorems.
Linear stability does not guarantee nonlinear stability, necessitating further investigation.
The research aims to establish criteria for the astrophysical viability of GB-scalarized black holes.
Limitations & open questions
Challenges include nonlinear mode coupling, backreaction effects, and loss of hyperbolicity.
The dynamical picture is complicated by the existence of multiple scalarized solutions.