A Field-Theory Approach for Modeling Dissipative Relativistic Fluids.

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.