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arXiv · 1807.02915

Tolman-like temperature gradients in stationary spacetimes

Jessica Santiago·Matt Visser
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Abstract

It is (or should be) well known that specification of a heat bath requires both a temperature and a 4-velocity, the rest frame of the heat bath. In static spacetimes there is a very natural and unique candidate for the 4-velocity of the heat bath, the normalized timelike Killing vector. However in stationary non-static spacetimes the situation is considerably more subtle, and several different "natural" 4-velocity fields suitable for characterizing the rest frame of a heat bath can be defined - thus Buchdahl's 1949 analysis for the Tolman temperature gradient in a stationary spacetime is only part of the story. In particular, the heat bath most suitable for describing the Hawking radiation from a rotating black hole is best described in terms of a gradient flow normal to the spacelike hypersurfaces, not in terms of Killing vectors.

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Jessica Santiago, Matt Visser. 2018-07-09. Tolman-like temperature gradients in stationary spacetimes. https://doi.org/10.1103/physrevd.98.064001

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