Scalarized black hole dynamics in Einstein-dilaton-Gauss-Bonnet gravity

We report on a numerical investigation of the stability of scalarized black holes in Einstein-dilaton-Gauss-Bonnet (EdGB) gravity in the full dynamical theory, though restricted to spherical symmetry. We find evidence that for sufficiently small curvature couplings the resulting scalarized black hole solutions are nonlinearly stable. For such small couplings, we show that an elliptic region forms inside these EdGB black hole spacetimes (prior to any curvature singularity), and give evidence that this region remains censored from asymptotic view. However, for coupling values ``superextremal'' relative to a given black hole mass, an elliptic region forms exterior to the horizon, implying the exterior Cauchy problem is ill-posed in this regime.