Gravitational thermodynamics of causal diamonds in (A)dS
Gravitational thermodynamics of causal diamonds in (A)dS
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DOI：
10.21468/scipostphys.7.6.079
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发表时间：
2018-12
期刊：
影响因子：
5.5
通讯作者：
T. Jacobson;Manus R. Visser
中科院分区：
文献类型：
--
作者：
T. Jacobson;Manus R. Visser
德西特时空的静态补丁和闵可夫斯基时空的林德勒楔是承认真正的基灵场的因果菱形，它们在引力扰动下表现为热力学平衡态。我们探讨的引力热力学扩展到所有的因果钻石在最大对称时空。虽然这样的菱形一般只允许一个共形基灵矢量，但这似乎在所有方面都是足够的。我们建立了一个Smarr公式，这样的钻石和“第一定律”的变化附近的解决方案。后者涉及边界面积、最大切片的空间体积、宇宙常数和物质哈密顿量的变化。总哈密顿量是沿着保持菱形的共形Killing向量演化的生成元。为了将第一定律解释为热力学关系，似乎有必要将负温度归因于钻石，就像先前对德西特时空静态补丁的特殊情况所建议的那样。包括量子校正，对于小钻石，我们恢复的“纠缠平衡”的结果，广义熵是固定的最大对称真空在固定的体积，我们重新制定了这与体积不固定的自由共形能量的平稳性。
The static patch of de Sitter spacetime and the Rindler wedge of Minkowski spacetime are causal diamonds admitting a true Killing field, and they behave as thermodynamic equilibrium states under gravitational perturbations. We explore the extension of this gravitational thermodynamics to all causal diamonds in maximally symmetric spacetimes. Although such diamonds generally admit only a conformal Killing vector, that seems in all respects to be sufficient. We establish a Smarr formula for such diamonds and a ``first law" for variations to nearby solutions. The latter relates the variations of the bounding area, spatial volume of the maximal slice, cosmological constant, and matter Hamiltonian. The total Hamiltonian is the generator of evolution along the conformal Killing vector that preserves the diamond. To interpret the first law as a thermodynamic relation, it appears necessary to attribute a negative temperature to the diamond, as has been previously suggested for the special case of the static patch of de Sitter spacetime. With quantum corrections included, for small diamonds we recover the ``entanglement equilibrium'' result that the generalized entropy is stationary at the maximally symmetric vacuum at fixed volume, and we reformulate this as the stationarity of free conformal energy with the volume not fixed.