Thermal Dynamics in General Relativity

Abstract

We discuss a relativistic model for heat conduction, building on a convective variational approach to multi-fluid systems where the entropy is treated as a distinct dynamical entity. We demonstrate how this approach leads to a relativistic version of the Cattaneo equation, encoding the finite thermal relaxation time that is required to satisfy causality. We also show that the model naturally includes the non-equilibrium Gibbs relation that is a key ingredient in most approaches to extended thermodynamics. Focussing on the pure heat conduction problem, we compare the variational results to the second-order model developed by Israel and Stewart. The comparison shows that, despite the very different philosophies behind the two approaches, the two models are equivalent at first order deviations from thermal equilibrium. Finally, we complete the picture by working out the non-relativistic limit of our results, making contact with recent work in that regime.

References in corpus (12)

• Relativistic Fluid Dynamics: Physics for Many Different Scales
• Causal Theories of Dissipative Relativistic Fluid Dynamics for Nuclear Collisions
• Gravitational waves from instabilities in relativistic stars
• Variational description of multi-fluid hydrodynamics: Uncharged fluids
• The Relaxation Effect in Dissipative Relativistic Fluid Theories
• A Relativistic Mean Field Model for Entrainment in General Relativistic Superfluid Neutron Stars
• Covariant analysis of Newtonian multi-fluid models for neutron stars: I Milne-Cartan structure and variational formulation
• Variational multi-fluid dynamics and causal heat conductivity
• Relativistic Two-stream Instability
• On the nature of the so-called generic instabilities in dissipative relativistic hydrodynamics
• Relativistic non-equilibrium thermodynamics revisited
• Entropy Production in Relativistic Hydrodynamics

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• Thermodynamics of uncharged relativistic multifluids
• Stability and causality of Carter's multifluid theory
• A covariant action principle for dissipative fluid dynamics: From formalism to fundamental physics
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• Dissipative relativistic magnetohydrodynamics of a multicomponent mixture and its application to neutron stars
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• Is Relativistic Hydrodynamics always Symmetric-Hyperbolic in the Linear Regime?
• Two Fluid Shear-Free Composites
• A variational approach to resistive relativistic plasmas
• Beyond ideal magnetohydrodynamics: Resistive, reactive and relativistic plasmas
• Local temperature in general relativity
• A minimal model for finite temperature superfluid dynamics
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• Linearizing a Non-linear Formulation for General Relativistic Dissipative Fluids
• Heat transport and diffusion in a canonical model of a relativistic gas
• Mapping GENERIC hydrodynamics into Carter's multifluid theory
• Heat propagation in rotating relativistic bodies
• Relativistic heat conduction in the large-flux regime
• Heat conduction in rotating relativistic stars
• Steady heat conduction in general relativity
• A molecular dynamics approach to dissipative relativistic hydrodynamics: propagation of fluctuations
• Temperature upper bound of an ideal gas
• Variational thermodynamics of relativistic thin disks
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• Multi-fluid Theory and Cosmology: A Convective Variational Approach to Interacting Dark-Sector
• The Cosmological Dipole in Tilted Anisotropic Universes
• Legendre symmetry and first order phase transitions of homogeneous systems
• Extending Israel and Stewart hydrodynamics to relativistic superfluids via Carter's multifluid approach
• A multifluid perspective on multimessenger modelling
• Putting gravity in control
• The geometry of induced currents in two dimensional media