Description
Title: Hairy Black Holes by Spontaneous Symmetry Breaking in ESGB theory
Abstract: We study hairy black hole solutions in Einstein-(Maxwell)-scalar-Gauss-Bonnet theory. The scalar coupling function includes quadratic and quartic terms, so the gravitational action has a U(1) symmetry. We argued that when the effective mass of the scalar field is at the critical value, hairy black holes are generated in a symmetry-broken vacuum via spontaneous symmetry breaking, where the Goldstone bosons are trivial. To examine such process, we introduce a scalar field perturbation on the newly formed background spacetime. We solve the linearized perturbation equation using Green’s function method. We begin by solving the Green’s function analytically, incorporating the branch cut contribution and then proceed to calculate the quasinormal modes (QNMs) numerically, which arise from the presence of poles in the Green’s function. These numerical results provide strong evidence for a dynamical process that unstable black holes without hairs transition into stable hairy black holes in the symmetry-broken phase through the spontaneous symmetry breaking. Moreover, we found that the spontaneous symmetry breaking associated with local U(1) is unlikely to occur in this theory.
