arXiv 0811.12682008-11hep-th

Einstein-Gauss-Bonnet引力下Taub-NUT/Bolt-AdS黑洞的热力学

Thermodynamics of Taub-NUT/Bolt-AdS Black Holes in Einstein-Gauss-Bonnet Gravity

A. Khodam-Mohammadi, M. Monshizadeh

备注：: 19 pages, 3 figures, some Refs. are added, Fig 1 is replaced, and some corrections are done
发表信息：: Phys.Rev.D79:044002,2009
DOI：: 10.1103/PhysRevD.79.044002

摘要：

本文在六维Einstein Gauss-Bonnet引力中讨论了参数为$α$的Taub-NUT/Bolt解的存在性.虽然具有基空间$S^{2}\times S^{2}$的时空在$r=N$处具有曲率奇点，这不允许NUT解，但我们可以进行与$\mathbb{CP}^{2}$情况相同的计算。研究了六维NUT/Bolt溶液的热力学性质。我们计算黑洞的有限作用量、质量、熵和温度。证明了热力学第一定律的正确性。结果表明，在NUT解中，通过代入$α^{\mathbb{CP}^{k}}=[(k+1)/k]α^{S^{2} \times S^{2}\times >...S_{k}^{2}}$，两个基空间的所有热力学量都是相互关联的.因此，通过研究$S^{2}\times S^{2}$情况下的NUT解决方案，未提供更多信息。这种关系对于螺栓解不成立。本文基于Gibbs-Duhem关系和NUT解的Gibbs自由能，用一种新的方法将黑洞热力学推广到任意偶数维。根据这一方法，将爱因斯坦引力中的广义有限作用量作为$α$的函数，再加上一个附加项，得到了爱因斯坦高斯-邦内有限作用量.通过研究$α$、$Λ$和$N$在允许范围内的热容和熵来进行稳定性分析。对于$d$维的NUT解，在$α$的窄范围内存在稳定相。在六维Bolt解中，度量对于$\mathcal{B}=S^{2}\times S^{2}$是完全稳定的，对于$\mathcal{B}=\mathbb{CP}^{2}$是完全不稳定的.

英文摘要：

We give a review of the existence of Taub-NUT/bolt solutions in Einstein Gauss-Bonnet gravity with the parameter $α$ in six dimensions. Although the spacetime with base space $S^{2}\times S^{2}$ has curvature singularity at $r=N$, which does not admit NUT solutions, we may proceed with the same computations as in the $\mathbb{CP}^{2}$ case. The investigation of thermodynamics of NUT/Bolt solutions in six dimensions is carried out. We compute the finite action, mass, entropy, and temperature of the black hole. Then the validity of the first law of thermodynamics is demonstrated. It is shown that in NUT solutions all thermodynamic quantities for both base spaces are related to each other by substituting $α^{\mathbb{CP}^{k}}=[(k+1)/k]α^{S^{2} \times S^{2}\times >...S_{k}^{2}}$. So no further information is given by investigating NUT solution in the $S^{2}\times S^{2}$ case. This relation is not true for bolt solutions. A generalization of the thermodynamics of black holes to arbitrary even dimensions is made using a new method based on the Gibbs-Duhem relation and Gibbs free energy for NUT solutions. According to this method, the finite action in Einstein Gauss-Bonnet is obtained by considering the generalized finite action in Einstein gravity with an additional term as a function of $α$. Stability analysis is done by investigating the heat capacity and entropy in the allowed range of $α$, $Λ$ and $N$. For NUT solutions in $d$ dimensions, there exist a stable phase at a narrow range of $α$. In six-dimensional Bolt solutions, metric is completely stable for $\mathcal{B}=S^{2}\times S^{2}$, and is completely unstable for $\mathcal{B}=\mathbb{CP}^{2}$ case.

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