Scalar-Gauss-Bonnet theories: Evasion of no-hair theorems and novel black-hole solutions

We consider a general Einstein-scalar-Gauss-Bonnet theory with a coupling function f(phi) between the scalar field and the quadratic gravitational Gauss-Bonnet term. We show that the existing no-hair theorems are easily evaded, and therefore black holes may emerge in the context of this theory. Indeed, we demonstrate that, under mild only assumptions for f(phi), asymptotic solutions describing either a regular black-hole horizon or an asymptotically-flat solution always emerge. We then show, through numerical integration, that the field equations allow for the smooth connection of these asymptotic solutions, and thus for the construction of a complete, regular black-hole solution with non-trivial scalar hair. We present and discuss the physical characteristics of a large number of such solutions for a plethora of coupling functions f(phi). Finally, we investigate whether pure scalar-Gauss-Bonnet black holes may arise in the context of our theory when the Ricci scalar may be altogether ignored.