Version 1
: Received: 31 May 2024 / Approved: 3 June 2024 / Online: 6 June 2024 (03:24:09 CEST)
Version 2
: Received: 14 July 2024 / Approved: 15 July 2024 / Online: 16 July 2024 (05:26:47 CEST)
How to cite:
Andersson, N.; Celora, T.; Comer, G.; Hawke, I. A Field-Theory Approach for Modeling Dissipative Relativistic Fluids. Preprints2024, 2024060082. https://doi.org/10.20944/preprints202406.0082.v2
Andersson, N.; Celora, T.; Comer, G.; Hawke, I. A Field-Theory Approach for Modeling Dissipative Relativistic Fluids. Preprints 2024, 2024060082. https://doi.org/10.20944/preprints202406.0082.v2
Andersson, N.; Celora, T.; Comer, G.; Hawke, I. A Field-Theory Approach for Modeling Dissipative Relativistic Fluids. Preprints2024, 2024060082. https://doi.org/10.20944/preprints202406.0082.v2
APA Style
Andersson, N., Celora, T., Comer, G., & Hawke, I. (2024). A Field-Theory Approach for Modeling Dissipative Relativistic Fluids. Preprints. https://doi.org/10.20944/preprints202406.0082.v2
Chicago/Turabian Style
Andersson, N., Gregory Comer and Ian Hawke. 2024 "A Field-Theory Approach for Modeling Dissipative Relativistic Fluids" Preprints. https://doi.org/10.20944/preprints202406.0082.v2
Abstract
We develop an action principle for producing a single fluid, two-constituent system with dissipation in general relativity. The two constituents in the model are particles and entropy. The particle flux creation rate is taken to be zero, while the entropy creation rate is non-zero. Building on previous work, it is demonstrated that a new term (the proper time derivative of the matter space ``metric'') is required in the Lagrangian in order to produce terms typically associated with bulk and shear viscosity. Equations of motion, entropy creation rate, and energy-momentum-stress tensor are derived. Using an Onsager approach of identifying thermodynamic ``forces'' and ``fluxes'' a model is produced which delivers the same entropy creation rate as the standard, relativistic Navier-Stokes equations. This result is then contrasted with a model generated in the spirit of the action principle, which takes as its starting point a specific Lagrangian and then produces the equations of motion, entropy creation rate, and energy-momentum-stress tensor. Unlike the equations derived from Onsager reasoning, where the analogs of the bulk and shear viscosity coefficients are prescribed ``externally'', we find that the form of the coefficients in the second example are a direct result of the specified Lagrangian. Furthermore, the coefficients are shown to satisfy evolution equations along the fluid worldline; also a product of the specific Lagrangian.
Keywords
relativistic fluids; dissipation; field theory
Subject
Physical Sciences, Astronomy and Astrophysics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
