具有多视界的静态拓扑伸缩子黑洞及其热力学性质
Static topological dilatonic black hole with multiple horizons and its thermodynamics
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中文总结 AI 辅助
该研究在爱因斯坦-伸缩子理论中结合非线性电磁场得到具有任意数量视界的静态拓扑带电黑洞解，分析其能量条件、热力学性质，发现其热行为更丰富，存在额外稳定相与三相点，还得到斯马尔关系。
中文摘要 AI 辅助
我们在爱因斯坦-伸缩子理论框架下，结合以麦克斯韦场不变量无穷级数形式表示的非线性电磁场，得到了一个静态拓扑带电黑洞解。与标准爱因斯坦-麦克斯韦-伸缩子（EMD）理论中黑洞最多仅有两个视界不同，该非线性推广理论可能产生具有任意数量视界的解。我们研究了能量条件，结果表明：对于非线性电磁场本身，所有能量条件在黑洞外部均被满足；而对于伸缩子场，黑洞外部未被违反的唯一条件是零能量条件（NEC）。我们还研究了该黑洞的热力学性质，发现其热行为比标准EMD理论对应的黑洞丰富得多。为完整描述热力学，我们采用欧氏方法，该方法可用于研究所谓的巨正则系综和正则系综，不同方法得到的结果具有一致性。欧氏描述自然地使我们能够研究全局稳定性，结果显示其与标准EMD解甚至雷斯纳-诺德斯特洛姆黑洞有一些共同特征，但非线性场会引发新的特殊性质，即可能存在额外的稳定相和一个三相点。为研究近临界行为，我们采用扩展相空间方法，其中宇宙学常数被视为热力学变量，利用该形式体系我们还得到了斯马尔关系。
英文摘要
We obtain a static topological charged black hole solution within Einstein-dilaton theory with nonlinear electromagnetic field represented by an infinite series over Maxwell field invariant. In contrast with standard Einstein-Maxwell-dilaton (EMD) theory where the black hole might have no more than two horizons, the nonlinear generalization might give rise to a solution with arbitrary number of horizons. We examine energy conditions and show that for the nonlinear electromagnetic field itself all the energy conditions are fulfilled outside of the black hole, whereas for the dilaton field the only condition which is not violated outside is the Null Energy Condition (NEC). We also study thermodynamics of the black hole and show that the thermal behaviour of the solution is considerably richer than for its standard EMD cousin. To have complete description of the thermodynamics we also use the Euclidean method, which allows us to consider the so-called Grand Canonical and Canonical Ensembles. The results obtained by different approaches show their consistency. The Euclidean description naturally allowed us to consider global stability, which is shown to have some common features with standard EMD solution, or even Reissner-Nordström black hole. But there some new peculiarities caused by the nonlinear field, namely we might have additional stable phases and a triple point. To examine near critical behaviour we consider the extended phase space approach, where the cosmological constant is supposed to be a thermodynamic variable. Making use of the extended formalism we also obtain the Smarr relation.
