Dynamics of a ℤ₂symmetric EdGB gravity in spherical symmetry

We report on a numerical investigation of black hole evolution in an Einstein dilaton Gauss-Bonnet (EdGB) gravity theory where the Gauss-Bonnet coupling and scalar (dilaton) field potential are symmetric under a global change in sign of the scalar field (a 'ℤ2' symmetry). We find that for sufficiently small Gauss-Bonnet couplings Schwarzschild black holes are stable to radial scalar field perturbations, and are unstable to such perturbations for sufficiently large couplings. For the latter case, we provide numerical evidence that there is a band of coupling parameters and black hole masses where the end states are stable scalarized black hole solutions, in general agreement with the results of Macedo et al (2019 Phys. Rev. D 99 104041). For Gauss-Bonnet couplings larger than those in the stable band, we find that an 'elliptic region' forms outside of the black hole horizon, indicating the theory does not possess a well-posed initial value formulation in that regime.