论文标题
宇宙学解决方案，新的灯芯旋转和热力学的第一定律
Cosmological Solutions, a New Wick-Rotation, and the First Law of Thermodynamics
论文作者
论文摘要
我们提出了欧几里得动作形式主义的改进实施，适合研究包含杀戮视野的一类宇宙学解决方案的热力学。为了获得确定签名的真正度量，我们通过分析延续所有类似空间的方向来执行“三重灯光旋转”。所得的欧几里得几何形状用于计算欧几里得在壳作用中，该作用定义了热力学潜力。我们表明，对于真空固定溶液，Einstein-Maxwell理论的平面解决方案以及先前发现的N = 2超级实力的宇宙学解决方案，可以使用这种热力学潜力来定义遵循体温动力学第一定律的内部能量。我们的方法是互补的，但与孤立的地平线形式主义一致。对于Einstein-Maxwell Solutions，我们在Einstein-Anti-Maxwell理论中发现了双重解决方案，其中Maxwell项的符号被逆转。这些解决方案是平面黑洞，而不是宇宙学的解决方案，而是在对相同的欧几里得作用和热力学关系的标准灯芯上产生的。
We present a modified implementation of the Euclidean action formalism suitable for studying the thermodynamics of a class of cosmological solutions containing Killing horizons. To obtain a real metric of definite signature, we perform a `triple Wick-rotation' by analytically continuing all space-like directions. The resulting Euclidean geometry is used to calculate the Euclidean on-shell action, which defines a thermodynamic potential. We show that for the vacuum de Sitter solution, planar solutions of Einstein-Maxwell theory and a previously found class of cosmological solutions of N = 2 supergravity, this thermodynamic potential can be used to define an internal energy which obeys the first law of thermodynamics. Our approach is complementary to, but consistent with the isolated horizon formalism. For planar Einstein-Maxwell solutions, we find dual solutions in Einstein-anti-Maxwell theory where the sign of the Maxwell term is reversed. These solutions are planar black holes, rather than cosmological solutions, but give rise, upon a standard Wick-rotation to the same Euclidean action and thermodynamic relations.
