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Linearizing a non-linear formulation for general relativistic dissipative fluids

Linearizing a non-linear formulation for general relativistic dissipative fluids
Linearizing a non-linear formulation for general relativistic dissipative fluids
Fully non-linear equations of motion for dissipative general relativistic fluids can be obtained from an action principle involving the explicit use of lower dimensional matter spaces. More traditional strategies for incorporating dissipation-like the famous Mueller-Israel-Stewart model-are based on expansions away from equilibrium defined, in part, by the laws of thermodynamics. The goal here is to build a formalism to facilitate comparison of the action-based results with those based on the traditional approach. The first step of the process is to use the action-based approach itself to build self-consistent notions of equilibrium. Next, first-order deviations are developed directly on the matter spaces, which motivates the latter as the natural arena for the underlying thermodynamics. Finally, we identify the dissipation terms of the action-based model with first-order "thermodynamic" fluxes, on which the traditional models are built. A simple application of a single viscous fluid is considered. The description is developed in a general setting so that the formalism can be used to describe more complicated systems, for which causal and stable models are not yet available. Finally, even though our expansions are halted at first order, we sketch out how a causal response can be implemented with telegraph-type equations.
gr-qc
0264-9381
Celora, Thomas
b15e9792-aae0-479a-83c5-b5c874b19fa6
Andersson, Nils
2dd6d1ee-cefd-478a-b1ac-e6feedafe304
Comer, Greg L.
e78ae434-e576-4b39-93cd-679b6f30432d
Celora, Thomas
b15e9792-aae0-479a-83c5-b5c874b19fa6
Andersson, Nils
2dd6d1ee-cefd-478a-b1ac-e6feedafe304
Comer, Greg L.
e78ae434-e576-4b39-93cd-679b6f30432d

Celora, Thomas, Andersson, Nils and Comer, Greg L. (2020) Linearizing a non-linear formulation for general relativistic dissipative fluids. Classical and Quantum Gravity. (doi:10.1088/1361-6382/abd7c1).

Record type: Article

Abstract

Fully non-linear equations of motion for dissipative general relativistic fluids can be obtained from an action principle involving the explicit use of lower dimensional matter spaces. More traditional strategies for incorporating dissipation-like the famous Mueller-Israel-Stewart model-are based on expansions away from equilibrium defined, in part, by the laws of thermodynamics. The goal here is to build a formalism to facilitate comparison of the action-based results with those based on the traditional approach. The first step of the process is to use the action-based approach itself to build self-consistent notions of equilibrium. Next, first-order deviations are developed directly on the matter spaces, which motivates the latter as the natural arena for the underlying thermodynamics. Finally, we identify the dissipation terms of the action-based model with first-order "thermodynamic" fluxes, on which the traditional models are built. A simple application of a single viscous fluid is considered. The description is developed in a general setting so that the formalism can be used to describe more complicated systems, for which causal and stable models are not yet available. Finally, even though our expansions are halted at first order, we sketch out how a causal response can be implemented with telegraph-type equations.

Text
2008.00945v1 - Accepted Manuscript
Restricted to Repository staff only until 31 December 2021.
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More information

Accepted/In Press date: 31 December 2020
e-pub ahead of print date: 31 December 2020
Additional Information: 57 pages RevTex, 2 pdf figures
Keywords: gr-qc

Identifiers

Local EPrints ID: 446055
URI: http://eprints.soton.ac.uk/id/eprint/446055
ISSN: 0264-9381
PURE UUID: 4da4350e-e12f-40c7-8373-6d6d0cdbfd84
ORCID for Nils Andersson: ORCID iD orcid.org/0000-0001-8550-3843

Catalogue record

Date deposited: 19 Jan 2021 17:34
Last modified: 26 Nov 2021 02:41

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Contributors

Author: Thomas Celora
Author: Nils Andersson ORCID iD
Author: Greg L. Comer

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