arXiv 0710.27092007-10gr-qchep-th

Einstein-Gauss-Bonnet引力中具有对称性的动力学黑洞

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

Masato Nozawa, Hideki Maeda

备注：: 13 pages, 1 figure, 5 tables; references added, typos corrected, accepted version in CQG
发表信息：: Class.Quant.Grav.25:055009,2008
DOI：: 10.1088/0264-9381/25/5/055009

摘要：

我们探讨了$n(\ge 5)$维Einstein-Gauss-Bonnet引力中由未来外捕获视界定义的动态黑洞的各个方面。本文假设时空具有对应于$(n-2)$维极大对称空间的等距对称性，并且Gauss-Bonnet耦合常数是非负的.根据广义相对论极限的存在与否，解被分为GR和非GR分支。在物质场为零能条件下，我们证明了在GR分支中，未来的外俘获视界具有与广义相对论相同的性质。与此相反，在非GR分支被证明是非类空的，其面积不增加到未来。我们可以认识到这种特殊的行为产生的事实，零能量条件必然导致零收敛条件径向零向量在GR分支，但不是在非GR分支。能量平衡定律产生了俘获视界的第一定律，由此我们可以读出俘获视界的熵，再现了Iyer-Wald的表达式。未来的外捕获视界的熵在沿其生成器的两个分支中都是不减的。

英文摘要：

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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英文摘要：

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