Riemann-Cartan Space-times of G\"odel Type

TL;DR

This paper investigates Riemann-Cartan G"odel-type space-times, deriving conditions for local homogeneity, classifying their symmetries, and analyzing their curvature and torsion properties.

Contribution

It generalizes previous Riemannian G"odel-type space-time classifications to include torsion, identifying symmetry groups and essential parameters for equivalence.

Findings

Space-times admit a five-dimensional affine-isometry group.

They are characterized by three parameters: ll, m^2, .

Algebraic types of curvature and torsion tensors are classified.

Abstract

A class of Riemann-Cartan G\"odel-type space-times are examined in the light of the equivalence problem techniques. The conditions for local space-time homogeneity are derived, generalizing previous works on Riemannian G\"odel-type space-times. The equivalence of Riemann-Cartan G\"odel-type space-times of this class is studied. It is shown that they admit a five-dimensional group of affine-isometries and are characterized by three essential parameters $\ell, m^2, \omega$: identical triads ($\ell, m^2, \omega$) correspond to locally equivalent manifolds. The algebraic types of the irreducible parts of the curvature and torsion tensors are also presented.