Evasion of No-Hair Theorems and Novel Black-Hole Solutions in Gauss-Bonnet Theories

TL;DR

This paper demonstrates that in Einstein-scalar-Gauss-Bonnet theories, black-hole solutions with scalar hair are common and can evade traditional no-hair theorems, expanding the landscape of possible black-hole configurations.

Contribution

It shows that regular, hairy black-hole solutions are generically possible in Einstein-scalar-Gauss-Bonnet theories, challenging existing no-hair theorems.

Findings

Existence of regular, asymptotically-flat black-hole solutions with scalar hair.

Evasion of traditional no-hair theorems in these theories.

Construction of numerous solutions for various coupling functions.

Abstract

We consider a general Einstein-scalar-GB theory with a coupling function f(\phi). We demonstrate that black-hole solutions appear as a generic feature of this theory since a regular horizon and an asymptotically-flat solution may be easily constructed under mild assumptions for f(\phi). We show that the existing no-hair theorems are easily evaded, and a large number of regular, black-hole solutions with scalar hair are then presented for a plethora of coupling functions f(\phi).