Analytic nondegenerate shift-symmetric Horndeski theories admit no static spherical regular black holes with a time-independent scalar; the unique marginal nonanalytic completion is sGB, whose hairy solutions remain centrally singular.
Instability of hairy black holes in regularized 4-dimensional Einstein-Gauss-Bonnet gravity
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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 spatially-flat maximally symmetric internal space are unstable against linear perturbations for any rescaled GB coupling constant. This instability is present for the angular propagation of even-parity perturbations both in the vicinity of an event horizon and at spatial infinity. There is also a strong coupling problem associated with the kinetic term of even-parity perturbations vanishing everywhere.
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Static regular black holes in Horndeski theories: analytic no-go and nonanalytic obstructions
Analytic nondegenerate shift-symmetric Horndeski theories admit no static spherical regular black holes with a time-independent scalar; the unique marginal nonanalytic completion is sGB, whose hairy solutions remain centrally singular.