We examine the relativistic
perfect fluid limit,
defined as the fastest possible local equilibration, in a medium with
polarizeability, defined as a non-zero local equilibrium partition of
angular momentum into spin and vorticity.
We show that the Lagrangian approach is best suited to analyzing this situation, as
it can be used to efficiently avoid issues such as the breakdown
of isotropy, the ambiguity of the energy-momentum tensor definition and
the lack of closure of conservation equations.
We obtain the Lagrangian and the equations of motion of an ideal
relativistic fluid with polarization, linearize them, and
show that to restore
causality a relaxation term linking vorticity and polarization,
analogous to the Israel-Stewart term linking viscous forces and
We close with an discussion of the phenomenological applicability
of the hydrodynamics with polarization developed here, focusing on the recent
finding of Lambda polarization and resonance spin alignement, and discussing
weather observables sensitive to early-time polarization exist.
Based on https://arxiv.org/abs/1807.02796
and previous work by the same authors