Perfect hypermomentum fluid: variational theory and equations of motion

TL;DR

This paper develops a variational framework for perfect hypermomentum fluids, deriving their equations of motion, matter currents, and evolution equations, extending fluid dynamics in metric-affine geometry.

Contribution

It introduces a new generalized Frenkel condition and formulates the variational theory for perfect hypermomentum fluids, including their equations of motion and matter currents.

Findings

Derived equations of motion for perfect hypermomentum fluid.

Established the form of matter currents in hypermomentum fluids.

Proved equivalence of fluid motion in metric-affine and Riemann spaces.

Abstract

The variational theory of the perfect hypermomentum fluid is developed. The new type of the generalized Frenkel condition is considered. The Lagrangian density of such fluid is stated, and the equations of motion of the fluid and the Weyssenhoff-type evolution equation of the hypermomentum tensor are derived. The expressions of the matter currents of the fluid (the canonical energy-momentum 3-form, the metric stress-energy 4-form and the hypermomentum 3-form) are obtained. The Euler-type hydrodynamic equation of motion of the perfect hypermomentum fluid is derived. It is proved that the motion of the perfect fluid without hypermomentum in a metric-affine space coincides with the motion of this fluid in a Riemann space.