Cosmological Solutions, a New Wick-Rotation, and the First Law of Thermodynamics

Gutowski, J, Mohaupt, T ORCID: 0000-0002-6864-4086 and Pope, G Cosmological Solutions, a New Wick-Rotation, and the First Law of Thermodynamics.

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Abstract

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.

Item Type:	Article
Additional Information:	77 pages including 27 pages of appendices, 10 figures
Uncontrolled Keywords:	hep-th, hep-th
Depositing User:	Symplectic Admin
Date Deposited:	06 Oct 2020 15:41
Last Modified:	18 Jan 2023 23:30
Related URLs:	Author
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3103712