Gauss-Bonnet black holes with nonconstant curvature horizons
Abstract
We investigate static and dynamical n(≥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 quasilocal mass that satisfies the unified first law, we show that most of the properties of the quasilocal 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 nonconstant. The quasilocal 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 nonzero cosmological constant, it cannot be globally stable for the positive cosmological constant.
- Publication:
-
Physical Review D
- Pub Date:
- June 2010
- DOI:
- 10.1103/PhysRevD.81.124007
- arXiv:
- arXiv:1004.0917
- Bibcode:
- 2010PhRvD..81l4007M
- Keywords:
-
- 04.50.Gh;
- 04.20.Cv;
- 04.50.-h;
- 04.70.Bw;
- Higher-dimensional black holes black strings and related objects;
- Fundamental problems and general formalism;
- Higher-dimensional gravity and other theories of gravity;
- Classical black holes;
- General Relativity and Quantum Cosmology;
- High Energy Physics - Theory
- E-Print:
- 15 pages, 1 figure