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Thermal dynamics in general relativity

Thermal dynamics in general relativity
Thermal dynamics in general relativity
We discuss a relativistic model for heat conduction, building on a convective variational approach to multi-fluid systems where the entropy is treated as a distinct dynamical entity. We demonstrate how this approach leads to a relativistic version of the Cattaneo equation, encoding the finite thermal relaxation time that is required to satisfy causality. We also show that the model naturally includes the non-equilibrium Gibbs relation that is a key ingredient in most approaches to extended thermodynamics. Focusing on the pure heat conduction problem, we compare the variational results with the second-order model developed by Israel and Stewart. The comparison shows that, despite the very different philosophies behind the two approaches, the two models are equivalent at first-order deviations from thermal equilibrium. Finally, we complete the picture by working out the non-relativistic limit of our results, making contact with recent work in that regime
1364-5021
738-759
Lopez-Monsalvo, C.S.
4131768d-9984-4fa4-a038-a0ad85095c87
Andersson, Nils
2dd6d1ee-cefd-478a-b1ac-e6feedafe304
Lopez-Monsalvo, C.S.
4131768d-9984-4fa4-a038-a0ad85095c87
Andersson, Nils
2dd6d1ee-cefd-478a-b1ac-e6feedafe304

Lopez-Monsalvo, C.S. and Andersson, Nils (2010) Thermal dynamics in general relativity. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 467 (2127), 738-759. (doi:10.1098/rspa.2010.0308).

Record type: Article

Abstract

We discuss a relativistic model for heat conduction, building on a convective variational approach to multi-fluid systems where the entropy is treated as a distinct dynamical entity. We demonstrate how this approach leads to a relativistic version of the Cattaneo equation, encoding the finite thermal relaxation time that is required to satisfy causality. We also show that the model naturally includes the non-equilibrium Gibbs relation that is a key ingredient in most approaches to extended thermodynamics. Focusing on the pure heat conduction problem, we compare the variational results with the second-order model developed by Israel and Stewart. The comparison shows that, despite the very different philosophies behind the two approaches, the two models are equivalent at first-order deviations from thermal equilibrium. Finally, we complete the picture by working out the non-relativistic limit of our results, making contact with recent work in that regime

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Published date: March 2010

Identifiers

Local EPrints ID: 181263
URI: http://eprints.soton.ac.uk/id/eprint/181263
ISSN: 1364-5021
PURE UUID: fe604fa8-147f-4dd6-97ff-45ae3e181c99
ORCID for Nils Andersson: ORCID iD orcid.org/0000-0001-8550-3843

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Date deposited: 15 Apr 2011 13:50
Last modified: 15 Mar 2024 02:59

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Contributors

Author: C.S. Lopez-Monsalvo
Author: Nils Andersson ORCID iD

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