Numerical Implementation of dissipative relativistic Hydrodynamics

REULA, O. A.; LEHNER, L.; RUBIO, M. E

Austin [WebConf]

Conferencia; 23rd Capra Meeting on Radiation Reaction in General Relativity; 2020

University of Texas at Austin

We develop a complete description of the class of conformal relativistic dissipative fluids of divergence form, following the formalism described in [R. Geroch and L. Lindblom, Phys. Rev. D 41, 1855 (1990), S. Pennisi, Some considerations on a non linear approach to extended thermodynamics and in Proceedings of Symposium of Kinetic Theory and Extended Thermodynamics, Bologna, 1987.]. This type of theory is fully described in terms of evolution variables whose dynamics are 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 and 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.