New hairy black-hole solutions with a dilaton potential

Abstract

We consider black-hole solutions with a dilaton field possessing a nontrivial potential approaching a constant negative value at infinity. The asymptotic behaviour of the dilaton field is assumed to be slower than that of a localized distribution of matter. A non-Abelian SU(2) gauge field is also included in the total action. The mass of the solutions admitting a power series expansion in 1/r at infinity and preserving the asymptotic anti-de Sitter geometry is computed by using a counterterm subtraction method. Numerical arguments are presented for the existence of hairy black-hole solutions for a dilaton potential of the form V(ϕ) = C1exp(2α1ϕ) + C2exp(2α2ϕ) + C3, special attention being paid to the case of the gauged supergravity model of Gates and Zwiebach.