Anisotropic matching principle for the hydrodynamics expansion

Understand

Following the recent success of anisotropic hydrodynamics we propose a new, general prescription for the hydrodynamics expansion around an anisotropic background.

• The anisotropic distribution is fixing exactly the complete energy-momentum tensor, just like the effective temperature is fixing the proper energy density in the ordinary expansion around local equilibrium.
• This means that momen- tum anisotropies are already included at the leading order, allowing for large pressure anisotropies without the need of a next to leading order treatment.
• The first moment of the Boltzmann equation (local four-momentum conservation) provides the time evolution of the proper energy density and the four velocity.