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arXiv 2203.01871hep-thgr-qc
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欧几里德de Sitter黑洞与微正则平衡

Euclidean de Sitter Black Holes and Microcanonical Equilibrium

Patrick Draper, Szilard Farkas

摘要:

Schwarzschild-de Sitter(SdS)黑洞不允许完全光滑的欧几里德延拓。我们讨论了一些修改的引力路径积分,使欧几里德SdS的半经典平衡的解释。首先,我们考虑“空腔中的引力”,将正则系综定义在一个切除一个视界的盒子中。然而,这种标准方法不适用于正的宇宙学常数:最低自由能的解具有负的热容,如果它要为正则配分函数提供领先的半经典贡献,这是不一致的。相反,我们修改边界条件的路径积分,以构建微正则配分函数,这似乎是定义良好的。然后,我们将两个系综相接触,并移除边界,产生一个更大的微正则系综的态,例如,同时包含黑洞和宇宙视界。这些系统是封闭的,没有边界,但它们必须具有某种形式的轻度度量间断。我们讨论了不连续性相当于插入一层薄的刚性膜的情况,将两个可以交换能量并处于局部平衡的系统分开。用这种方法得到的平衡位形如果含有一个黑洞,则是不稳定的。

英文摘要:

Schwarzschild-de Sitter (SdS) black holes do not admit a completely smooth Euclidean continuation. We discuss some modifications of the gravitational path integral that give Euclidean SdS a semiclassical equilibrium interpretation. First we consider "gravity in a cavity," defining the canonical ensemble in a box that excises one horizon. However, this standard approach does not work for positive cosmological constant: the solution of lowest free energy has a negative heat capacity, which is inconsistent if it is to provide the leading semiclassical contribution to a canonical partition function. Instead we modify the boundary conditions in the path integral to construct the microcanonical partition function, which appears to be well-defined. We then bring two ensembles into contact and remove the boundary, producing states of a larger microcanonical ensemble that contain, for example, both a black hole and a cosmological horizon at once. These systems are closed and have no boundary, but they must possess some form of mild metric discontinuity. We discuss the case where the discontinuity is equivalent to the insertion of a thin, rigid membrane, separating two systems that can exchange energy and are at local equilibrium. Equilibrium configurations obtained in this way are found to be thermodynamically unstable if they contain a black hole.

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