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arXiv · 1004.0917

Gauss-Bonnet black holes with non-constant curvature horizons

Hideki Maeda
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Abstract

We investigate static and dynamical n(\ge 6)-dimensional black holes in Einstein-Gauss-Bonnet gravity of which horizons have the isometries of an (n-2)-dimensional Einstein space with a condition on its Weyl tensor originally given by Dotti and Gleiser. Defining a generalized Misner-Sharp quasi-local mass that satisfies the unified first law, we show that most of the properties of the quasi-local mass and the trapping horizon are shared with the case with horizons of constant curvature. It is shown that the Dotti-Gleiser solution is the unique vacuum solution if the warp factor on the (n-2)-dimensional Einstein space is non-constant. The quasi-local mass becomes constant for the Dotti-Gleiser black hole and satisfies the first law of the black-hole thermodynamics with its Wald entropy. In the non-negative curvature case with positive Gauss-Bonnet constant and zero cosmological constant, it is shown that the Dotti-Gleiser black hole is thermodynamically unstable. Even if it becomes locally stable for the non-zero cosmological constant, it cannot be globally stable for the positive cosmological constant.

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Hideki Maeda. 2010-12-23. Gauss-Bonnet black holes with non-constant curvature horizons. https://doi.org/10.1103/physrevd.81.124007

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