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arXiv 2309.06293gr-qchep-th
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参考系与黑洞热力学

Reference Frames and Black Hole Thermodynamics

Franco Fiorini, P. A. González, Yerko Vásquez

备注：
Accepted for publication in JCAP
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AI总结：

本文研究绝对平行引力中挠率表面项与 Gibbons-Hawking-York 边界项的关系，发现其等价性依赖于标架选择，并找到一类适应 Schwarzschild 时空的标架，可在无需背景减除的情况下正确给出黑洞熵和引力能量。

摘要：

在广义相对论的绝对平行表述中，由于标量曲率可以写成纯挠率形式，长期以来人们知道作用量中会出现一个仅基于挠率张量的表面项。后来有人提出，这一项可能扮演 Gibbons-Hawking-York 边界项的角色，而后者在路径积分方法中与自由能相关，进而通过标准热力学论证与黑洞熵相联系。我们表明，这两个边界项的等同关系相当不完整，并且强烈依赖于用于重现给定度规的标架（tetrad）场的选择。通过考虑标架场的变分，且不要求其满足边界面上类似 Dirichlet 的条件，我们找到了一类适应 Schwarzschild 时空的标架，在其中 Gibbons-Hawking-York 与挠率之间的联系实际上得以建立，并且无需任何背景减除即可得到正确的黑洞熵。值得注意的是，这些标架还使得由 teleparallel 能量-动量赝流计算出的引力能量具有正确数值。

英文摘要：

In the context of the absolute parallelism formulation of General Relativity, and because of the fact that the scalar curvature can be written in purely torsional terms, it was known for a long time that a surface term based solely on the torsion tensor appears in the action. It was subsequently suggested that this term might play the role of the Gibbons-Hawking-York boundary term which, in turn, is associated to the free energy in the path integral approach, and then, to the black hole entropy by standard thermodynamic arguments. We show that the identification of the two boundary terms is rather incomplete, and that it strongly depends on the choice of the tetrad (frame) field used to reproduce a given metric. By considering variations of the tetrad field not necessarily subjected to Dirichlet-like conditions on the boundary surface, we find a class of frames adapted to the Schwarzschild spacetime in which the Gibbons-Hawking-York/torsion link is actually established, and conducing to the right black hole entropy without the need of any background subtraction. Remarkably, these frames are also responsible for the correct value of the gravitational energy as computed from the teleparallel energy-momentum pseudo-current.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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