New hairy black hole solutions with a dilaton potential

TL;DR

This paper introduces new black hole solutions with a dilaton field and nonabelian gauge fields in anti-de Sitter space, demonstrating their existence through numerical methods and analyzing their properties within specific supergravity models.

Contribution

It presents novel hairy black hole solutions with a dilaton potential in anti-de Sitter space, including numerical evidence and analysis within a specific supergravity framework.

Findings

Existence of hairy black hole solutions with a dilaton potential.

Solutions preserve asymptotic anti-de Sitter geometry.

Mass computed via counterterm subtraction method.

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 $V(\phi)=C_1 \exp(2\alpha_1 \phi)+C_2 \exp(2\alpha_2 \phi)+C_3$, special attention being paid to the case of ${\cal N}=4, D=4$ gauged supergravity model of Gates and Zwiebach.