Dynamical black holes with symmetry in Einstein-Gauss-Bonnet gravity

Details Dynamical black holes with symmetry in Einstein-Gauss-Bonnet gravity Dynamical black holes with symmetry in Einstein-Gauss-Bonnet gravity

2007-10-15

arxiv.org/abs/0710.2709v3

Class.Quant.Grav.25:055009,2008

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

13 pages, 1 figure, 5 tables; references added, typos corrected, accepted version in CQG

Scientific paper

10.1088/0264-9381/25/5/055009

We explore various aspects of dynamical black holes defined by a future outer trapping horizon in $n(\ge 5)$-dimensional Einstein-Gauss-Bonnet gravity. In the present paper, we assume that the spacetime has symmetries corresponding to the isometries of an $(n-2)$-dimensional maximally symmetric space and the Gauss-Bonnet coupling constant is non-negative. Depending on the existence or absence of the general relativistic limit, solutions are classified into GR and non-GR branches, respectively. Assuming the null energy condition on matter fields, we show that a future outer trapping horizon in the GR branch possesses the same properties as that in general relativity. In contrast, that in the non-GR branch is shown to be non-spacelike with its area non-increasing into the future. We can recognize this peculiar behavior to arise from a fact that the null energy condition necessarily leads to the null convergence condition for radial null vectors in the GR branch, but not in the non-GR branch. The energy balance law yields the first law of a trapping horizon, from which we can read off the entropy of a trapping horizon reproducing Iyer-Wald's expression. The entropy of a future outer trapping horizon is shown to be non-decreasing in both branches along its generator.

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