Instantaneous Temperatures \`a la Hadamard: Towards a generalized Stefan-Boltzmann law for curved spacetime
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.
Keywords
Cite
@article{arxiv.1804.05382,
title = {Instantaneous Temperatures \`a la Hadamard: Towards a generalized Stefan-Boltzmann law for curved spacetime},
author = {Aditya Dhumuntarao and José Tomás Gálvez Ghersi and Niayesh Afshordi},
journal= {arXiv preprint arXiv:1804.05382},
year = {2018}
}
Comments
REVTeX 4.1, 10 pages, 2 figures. Considered effects from higher order terms in the quasi-local expansion. Minor typos fixed, conclusions revised