Linearizing a non-linear formulation for general relativistic dissipative fluids

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.

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Identifiers

ORCID for Thomas Celora: orcid.org/0000-0002-6515-3644

ORCID for Nils Andersson: orcid.org/0000-0001-8550-3843

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