Anisotropic fluid dynamics in the early stage of relativistic heavy-ion collisions

A formalism for anisotropic fluid dynamics is proposed. It is designed to describe boost-invariant systems with anisotropic pressure. Such systems are expected to be produced at the early stages of relativistic heavy-ion collisions, when the timescales are too short to achieve equal thermalization of transverse and longitudinal degrees of freedom. The approach is based on the energy-momentum and entropy conservation laws, and may be regarded as a minimal extension of the boost-invariant standard relativistic hydrodynamics of the perfect fluid. We show how the formalism may be used to describe the isotropization of the system (the transition from the initial state with no longitudinal pressure to the final state with equal longitudinal and transverse pressure).