Rectifying no-hair theorems in Gauss-Bonnet theory

Abstract

We revisit the no-hair theorems in Einstein-Scalar-Gauss-Bonnet theory with a general coupling function between the scalar and the Gauss-Bonnet term in four dimensional spacetime. We first resolve the conflict caused from the incomplete derivation of the old no-hair theorem by taking into account the surface term and restore its reliability. We also clarify that the novel no-hair theorem is always evaded for regular black hole solutions without any restrictions as long as the regularity conditions are satisfied.