General relativistic spinning fluids with a modified projection tensor

TL;DR

This paper derives a new energy-momentum tensor for relativistic spinning fluids compatible with a specific supplementary condition, modifies the perfect-fluid model, and demonstrates its applicability in cosmological solutions like Friedmann-Robertson-Walker space-time.

Contribution

It introduces a novel energy-momentum tensor for relativistic spinning fluids based on a general Lagrangian and modifies the perfect-fluid model with a new projection tensor.

Findings

The derived tensor is compatible with Tulczyjew-type conditions.

Equations of motion admit Friedmann-Robertson-Walker solutions.

The tensor combines Belinfante-Rosenfeld and modified perfect-fluid components.

Abstract

An energy-momentum tensor for general relativistic spinning fluids compatible with Tulczyjew-type supplementary condition is derived from the variation of a general Lagrangian with unspecified explicit form. This tensor is the sum of a term containing the Belinfante-Rosenfeld tensor and a modified perfect-fluid energy-momentum tensor in which the four-velocity is replaced by a unit four-vector in the direction of fluid momentum. The equations of motion are obtained and it is shown that they admit a Friedmann-Robertson-Walker space-time as a solution.