Instability of hairy black holes in regularized 4-dimensional Einstein-Gauss-Bonnet gravity

Abstract

In regularized 4-dimensional Einstein-Gauss-Bonnet (EGB) gravity derived from a Kaluza-Klein reduction of higher-dimensional EGB theory, we study the existence and stability of black hole (BH) solutions on a static and spherically symmetric background. We show that asymptotically-flat hairy BH solutions realized for a flat internal maximally symmetric space are unstable against linear perturbations for any rescaled GB coupling constant. The propagation of even-parity perturbations for high angular momentum modes plays a crucial role to reach the conclusion of BH instability in the vicinity of an event horizon.