Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2008-05-27
Phys.Rev.D78:041503,2008
Physics
High Energy Physics
High Energy Physics - Theory
5 pages, no figures; v2, revised version, references added; v3, final version to appear in Physical Review D
Scientific paper
10.1103/PhysRevD.78.041503
In this paper, the following two propositions are proven under the dominant energy condition for the matter field in the higher-dimensional spherically symmetric spacetime in Einstein-Gauss-Bonnet gravity in the presence of a cosmological constant $\Lambda$. First, for $\Lambda\le 0$ and $\alpha \ge 0$ without a fine-tuning to give a unique anti-de Sitter vacuum, where $\alpha$ is the Gauss-Bonnet coupling constant, vanishing generalized Misner-Sharp mass is equivalent to the maximally symmetric spacetime. Under the fine-tuning, it is equivalent to the vacuum class I spacetime. Second, under the fine-tuning with $\alpha>0$, the asymptotically anti-de Sitter spacetime in the higher-dimensional Henneaux-Teitelboim sense is only a special class of the vacuum class I spacetime. The latter means the universal slow fall-off to the unique anti-de Sitter infinity in the presence of physically reasonable matter.
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