Relativistic third-order dissipative fluid dynamics from kinetic theory

We present the derivation of a novel third-order hydrodynamic evolution equation for the shear stress tensor from kinetic theory. The Boltzmann equation with a relaxation time approximation for the collision term is solved iteratively using a Chapman-Enskog-like expansion to obtain the nonequilibrium phase-space distribution function. Subsequently, the evolution equation for the shear stress tensor is derived from its kinetic definition up to third order in gradients. We quantify the significance of the new derivation within a one-dimensional scaling expansion and demonstrate that the results obtained using the third-order viscous equations derived here provides a very good approximation to the exact solution of the Boltzmann equation in a relaxation time approximation. We also show that the time evolution of pressure anisotropy obtained using our equations is in better agreement with transport results than that obtained with an existing third-order calculation based on the second law of thermodynamics.