2020/08/16 by J. Gutowski, Thomas Mohaupt, Gutowski, J. +5 · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories #hep-th
paper · pdf · doi:10.48550/arxiv.2008.06929
80 pages including 27 pages of appendices, 10 figures. Revised version: extended discussion of related results, several references added. Accepted for publication in JHEP
openalex publication_date 2020/08/16 · arxiv created 2021/02/16 · arxiv updated 2021/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.