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A Field-Theory Approach for Modeling Dissipative Relativistic Fluids.

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  • 1Mathematical Sciences and STAG Research Centre, University of Southampton, Southampton SO17 1BJ, UK.

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Summary

We developed an action principle for relativistic fluids with dissipation, incorporating particle and entropy constituents. This approach naturally yields viscosity coefficients, unlike traditional methods.

Keywords:
dissipationfield theoryrelativistic fluids

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Area of Science:

  • Physics
  • General Relativity
  • Fluid Dynamics

Background:

  • Dissipative phenomena in relativistic fluids are crucial for astrophysical and cosmological models.
  • Existing models often rely on phenomenological descriptions or external prescriptions for transport coefficients.

Purpose of the Study:

  • To formulate a first-principles action principle for a single-fluid, two-constituent system (particles and entropy) in general relativity.
  • To derive equations of motion, entropy production, and the energy-momentum-stress tensor from this principle.
  • To investigate the origin and nature of dissipative coefficients like bulk and shear viscosity.

Main Methods:

  • Construction of a Lagrangian incorporating a novel term: the proper time derivative of the matter space metric.
  • Derivation of field equations, entropy creation rate, and energy-momentum-stress tensor.
  • Comparison of results with the Onsager reciprocal relations approach and relativistic Navier-Stokes equations.

Main Results:

  • The action principle naturally generates terms associated with bulk and shear viscosity.
  • A model derived from the action principle yields the same entropy creation rate as relativistic Navier-Stokes equations.
  • Unlike Onsager-based models, viscosity coefficients emerge intrinsically from the Lagrangian and satisfy evolution equations.

Conclusions:

  • The developed action principle provides a consistent framework for describing dissipative relativistic fluids.
  • This approach offers a deeper, first-principles understanding of viscosity in such systems.
  • The intrinsic derivation of transport coefficients suggests a more fundamental description of fluid dynamics in general relativity.