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arXiv 1503.00974gr-qchep-thmath-phmath.MP
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具有视界拓扑的静态纯Lovelock黑洞解${\bf S^{(n)} \times S^{(n)}}$

Static pure Lovelock black hole solutions with horizon topology ${\bf S^{(n)} \times S^{(n)}}$

Naresh Dadhich, Josep M. Pons

备注：
21 pages. Matches JHEP published version
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摘要：

众所周知，静态时空中任意Lovelock阶的真空方程最终可化为一个代数方程，我们证明了对于拓扑${\bf S^{(n)} \times S^{(n)}}$，任意阶$N$的纯Lovelock引力也是如此.因此，我们获得了纯Lovelock静态黑洞解与两球拓扑结构的任何顺序$N$，特别是我们研究了全面详细的第三和第四阶Lovelock黑洞。值得注意的是，黑洞的热力学稳定性区分了$N$的奇偶性，从而区分了正$Λ$和负$Λ$，并且偏向于前者而排斥后者。

英文摘要：

It is well known that vacuum equation of arbitrary Lovelock order for static spacetime ultimately reduces to a single algebraic equation, we show that the same continues to hold true for pure Lovelock gravity of arbitrary order $N$ for topology ${\bf S^{(n)} \times S^{(n)}}$. We thus obtain pure Lovelock static black hole solutions with two-sphere topology for any order $N$, and in particular we study in full detail the third and fourth order Lovelock black holes. It is remarkable that thermodynamical stability of black hole discerns between odd and even $N$, and consequently between negative and positive $Λ$ and it favours the former while rejecting the latter.

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