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In regularized 4-dimensional Einstein-Gauss-Bonnet (EGB) gravity derived froma Kaluza-Klein reduction of higher-dimensional EGB theory, we study theexistence and stability of black hole (BH) solutions on a static andspherically symmetric background. We show that asymptotically-flat hairy BHsolutions realized for a spatially-flat maximally symmetric internal space areunstable against linear perturbations for any rescaled GB coupling constant.This instability is present for the angular propagation of even-parityperturbations both in the vicinity of an event horizon and at spatial infinity.There is also a strong coupling problem associated with the kinetic term ofeven-parity perturbations vanishing everywhere.

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