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arXiv · 1804.05382

Instantaneous Temperatures \`a la Hadamard: Towards a generalized Stefan-Boltzmann law for curved spacetime

Aditya Dhumuntarao·José Tomás Gálvez Ghersi·Niayesh Afshordi
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Abstract

In the celebrated Unruh effect, we learn that a uniformly accelerating detector in a Minkowski vacuum spacetime registers a constant temperature. Building on prior work, we present a technique based on derivative couplings of the two-point Wightman function and the Hadamard renormalization procedure to define an instantaneous temperature for a massive scalar field, non-minimally coupled to gravity. We find the temperature contains local contributions from the acceleration of the detector, the curvature of spacetime, and the renormalized stress-energy tensor of the field. Our result, which can be considered as a generalized Stefan-Boltzmann law for curved spacetimes, agrees with the familiar expressions found in 4D Rindler, thermal Minkowski, and de Sitter.

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Aditya Dhumuntarao, José Tomás Gálvez Ghersi, Niayesh Afshordi. 2018-04-15. Instantaneous Temperatures \`a la Hadamard: Towards a generalized Stefan-Boltzmann law for curved spacetime. https://arxiv.org/abs/1804.05382

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