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 nonabelian 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 $V(\varphi )=C_1\exp (2{\alpha }_1\varphi )+C_2\exp (2{\alpha }_2\varphi )+C_3$, special attention being paid to the case of $\mathcal{N}=4,D=4$ gauged supergravity model of Gates and Zwiebach.

12 pages, 4 figures; v2:references added, typos corrected, small changes in Section 4

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