Rectifying No-Hair Theorems in Gauss-Bonnet theory

TL;DR

This paper revisits and clarifies the conditions under which no-hair theorems in Einstein-Scalar-Gauss-Bonnet theory hold or are evaded, emphasizing the importance of surface terms and regularity conditions.

Contribution

It demonstrates that the old no-hair theorem's surface term is crucial and shows that the novel no-hair theorem can be evaded for regular black holes without restrictions.

Findings

Surface term is crucial when coupling function does not vanish at infinity.

Old no-hair theorem can be invalidated by considering surface contributions.

Regular black hole solutions evade the no-hair theorem under regularity conditions.

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. In the case of the old no-hair theorem the surface term has so far been ignored, but this plays a crucial role when the coupling function does not vanish at infinity and the scalar field admits a power expansion with respect to the inverse of the radial coordinate in that regime. 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.