  Hydrodynamics is a general theoretical framework for describing the long-time
large-distance behaviors of various macroscopic physical systems, with its
equations based on conservation laws such as energy-momentum conservation and
charge conservation. Recently there has been significant interest in
understanding the implications of angular momentum conservation for a
corresponding hydrodynamic theory. In this work, we examine the key conceptual
issues for such a theory in the relativistic regime where the orbital and spin
components get entangled. We derive the equations for relativistic viscous
hydrodynamics with angular momentum through Navier-Stokes type of gradient
expansion analysis and find five new transport coefficients for angular
momentum diffusion modes.
