A New Class of Exact Hairy Black Hole Solutions

Details A New Class of Exact Hairy Black Hole Solutions A New Class of Exact Hairy Black Hole Solutions

2009-11-09

arxiv.org/abs/0911.1711v2

Gen.Rel.Grav.43:163-180,2011

Physics

High Energy Physics

High Energy Physics - Theory

18 pages, 6 figures, minor changes, references added, published version

Scientific paper

10.1007/s10714-010-1079-0

We present a new class of black hole solutions with minimally coupled scalar field in the presence of a negative cosmological constant. We consider a one-parameter family of self-interaction potentials parametrized by a dimensionless parameter $g$. When $g=0$, we recover the conformally invariant solution of the Martinez-Troncoso-Zanelli (MTZ) black hole. A non-vanishing $g$ signals the departure from conformal invariance. All solutions are perturbatively stable for negative black hole mass and they may develop instabilities for positive mass. Thermodynamically, there is a critical temperature at vanishing black hole mass, where a higher-order phase transition occurs, as in the case of the MTZ black hole. Additionally, we obtain a branch of hairy solutions which undergo a first-order phase transition at a second critical temperature which depends on $g$ and it is higher than the MTZ critical temperature. As $g\to 0$, this second critical temperature diverges.

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