Locally Rotationally Symmetric Spacetimes in Einstein-Cartan Theory and Their Classification

TL;DR

This paper derives covariant equations for locally rotationally symmetric torsion spacetimes in Einstein-Cartan theory, classifies these spacetimes into distinct categories, and finds new analytical solutions to their gravitational field equations.

Contribution

It provides a complete covariant framework and classification scheme for LRS torsion spacetimes in Einstein-Cartan theory, including new analytical solutions.

Findings

Classification scheme for LRS torsion spacetimes

Explicit properties of each class analyzed

New analytical solutions obtained

Abstract

We present the complete set of covariant equations that govern the locally rotationally symmetric torsion spacetimes sourced by Weyssenhoff fluid in Einstein-Cartan-Sciama-Kibble gravity. Using these equations, we can explore in detail the peculiar relationship between conformal structure and torsion. We develop a comprehensive scheme to categorize these torsional spacetimes into distinct classes. We explicitly analyze the properties of each class and obtain novel analytical solutions to the gravitational field equations.