Traditionally, second order viscous hydrodynamics has been used to reproduce the soft collective flow and hadronic spectra in heavy-ion collisions; however, due to the rapid longitudinal expansion in the early stages of evolution, the the quark gluon plasma (QGP) produced in heavy-ion colisions may posses substantial pressure anisotropies.
These large viscous corrections violate the viscous hydrodynamics assumption of small deviations from local equilibrium. In order to more accurately treat systems possessing such large deviations from equilibrium, a new approach was developed, called anisotropic hydrodynamics (aHydro). In this approach the pressure anisotropy is treated in an non-perturbative way at the leading order of the hydrodynamics expansion. This allows to have an already striking agreement between aHydro and the exact solutions of the Boltzmann equation already at the leading order.
In second order viscous hydrodynamics there are different prescriptions to extract the transport coefficients. In a similar way, for the hydrodynamics expansion around an anisotropic background, there is more than one way for taking into account the pressure anisotropy, and for treating the next to leading order corrections. We will present the latest prescriptions for anisotropic hydrodynamics, which are no longer relying on any simplifying symmetry assumption, like longitudinal boost invariance or homogeneity on the transverse plane.
