The variational theory of the perfect dilaton-spin fluid in a Weyl-Cartan space

TL;DR

This paper develops a variational framework for a perfect fluid with intrinsic spin and dilatonic charge in a Weyl-Cartan space, deriving equations of motion, conservation laws, and matter currents.

Contribution

It introduces a new variational formulation for dilaton-spin fluids in Weyl-Cartan geometry, including equations of motion and conserved quantities.

Findings

Derived equations of motion for the fluid.

Established conservation law of dilatonic charge.

Obtained explicit expressions for matter currents.

Abstract

The variational theory of the perfect fluid with intrinsic spin and dilatonic charge (dilaton-spin fluid) is developed. The spin tensor obeys the classical Frenkel condition. The Lagrangian density of such fluid is stated, and the equations of motion of the fluid, the Weyssenhoff-type evolution equation of the spin tensor and the conservation law of the dilatonic charge 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 dilaton-spin momentum 3-form) are obtained.