Linearizing a non-linear formulation for general relativistic dissipative fluids
- 31 December 2020
- journal article
- research article
- Published by IOP Publishing in Classical and Quantum Gravity
- Vol. 38 (6), 065009
- https://doi.org/10.1088/1361-6382/abd7c1
Abstract
Fully non-linear equations of motion for dissipative general relativistic multi-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 Muller-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 construct 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 "thermodynamical" fluxes, on which the traditional models are built. The description is developed in a general setting so that the formalism can be used to describe multi-fluid systems, for which causal and stable models are not yet available. As an illustration of the approach, a simple application of a single viscous fluid is considered and, even though the expansion is halted at first order, we sketch how a causal response can be implemented through Cattaneo-type equations.Keywords
Funding Information
- Science and Technology Facilities Council (ST/R00045X/1)
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