A hyperbolic theory of relativistic conformal dissipative fluids

Abstract

We develop a complete description of the class of conformal relativistic dissipative fluids of divergence form, following the formalism carried out by Geroch, Lindblom and Pennisi. This type of theories is fully described in terms of evolution variables whose dynamics is governed by total divergence-type conservation laws. Specifically, we give a characterization of the whole family of conformal fluids in terms of a single master scalar function defined up to second order corrections in dissipative effects, which we explicitly find in general form. This allows us to identify the equilibrium states of the theory, as well as to derive constitutive relations and a Fourier-like law for the corresponding first-order theory heat flux. Finally, we show that among this class of theories-- and near equilibrium configurations-- there exist symmetric hyperbolic ones, implying that for them one can define well posed initial value problems.

arXiv comment48 pages, no figures

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• Nonlinear causality of general first-order relativistic viscous hydrodynamics
• Theories of Relativistic Dissipative Fluid Dynamics
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• Evolutions in first-order viscous hydrodynamics
• A new continuum model for general relativistic viscous heat-conducting media
• Fully developed relativistic turbulence
• Relativistic viscous effects on the primordial gravitational waves spectrum
• On Extended Thermodynamics: From Classical to the Relativistic Regime
• Linearized dispersion relations in viscous relativistic hydrodynamics
• Nonlinear Fluctuations in Relativistic Causal Fluids
• Fluid-gravity correspondence and causal first-order relativistic viscous hydrodynamics
• Breakdown of smooth solutions to the Müller-Israel-Stewart equations of relativistic viscous fluids
• Field Theory Approaches to Relativistic Hydrodynamics
• Field redefinition and its impact in relativistic hydrodynamics
• Numerical simulations of divergence-type theories for conformal dissipative fluids
• Primordial Weibel instability
• Constraint evolution in first-order viscous relativistic fluids
• Nonlinear Dynamics of Tensor Modes in Conformal Real Relativistic Fluids