Linearizing a nonlinear formulation for general relativistic dissipative fluids
Abstract
Fully nonlinear equations of motion for dissipative general relativistic multifluids 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 MüllerIsraelStewart 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 actionbased results with those based on the traditional approach. The first step of the process is to use the actionbased approach itself to construct selfconsistent notions of equilibrium. Next, firstorder 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 actionbased model with firstorder ‛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 multifluid 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 Cattaneotype equations.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 March 2021
 DOI:
 10.1088/13616382/abd7c1
 arXiv:
 arXiv:2008.00945
 Bibcode:
 2021CQGra..38f5009C
 Keywords:

 general relativity;
 dissipative fluids;
 action principle;
 General Relativity and Quantum Cosmology
 EPrint:
 Final version as published on Classical and Quantum Gravity