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

We consider a general Einstein-scalar-Gauss-Bonnet 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).