Extended Thermodynamics in Relativistic Accretion Flow

Accretion onto compact objects is a prominent astrophysical process involving non-ideal fluid flow in strong gravity. The generic description is presently by the relativistic Navier-Stokes-Fourier equations. This theory, however, predicts that fluctuations in the dissipative variables (i.e., the heat flux and the shear stresses) propagate at causality violating, infinite speeds and that the thermodynamic equilibrium states are unstable. This behavior is problematic particularly for systems that undergo rapid variablity, on timescales shorter than or comparable to the dissipative relaxation times (a condition naturally met in highly relativistic flow). These difficulties are removed in extended dissipative fluid theories, where the constraints that determine the dissipative variables in the conventional theory are replaced by causal evolution equations. We review the basic field equations of a particular extended theory which has been recently formulated in the 3+1 framework appropriate for numerical implementation. We briefly discuss its application to turbulent systems such as accretion discs.