On a Class of Riemann-Cartan Space-times of G\"odel Type

TL;DR

This paper analyzes a specific class of G"odel-type space-times within Riemann-Cartan geometry using computer algebra, deriving conditions for their homogeneity and symmetry properties, and connecting to previous Riemannian results.

Contribution

It provides a coordinate-invariant description and new conditions for space-time homogeneity of Riemann-Cartan G"odel-type space-times, extending prior work.

Findings

Identified conditions for space-time homogeneity.

Classified symmetry groups of the space-times.

Connected Riemann-Cartan results to classical Riemannian cases.

Abstract

A class of Riemann-Cartan G\"odel-type space-times is examined by using the equivalence problem techniques, as formulated by Fonseca-Neto et al. and embodied in a suite of computer algebra programs called TCLASSI. A coordinate-invariant description of the gravitational field for this class of space-times is presented. It is also shown that these space-times can admit a group $G_{r}$ of affine-isometric motions of dimensions $r=2, 4, 5$. The necessary and sufficient conditions for space-time (ST) homogeneity of this class of space-times are derived, extending previous works on G\"odel-type space-times. The equivalence of space-times in the ST homogeneous subclass is studied, recovering recent results under different premises. The results of the limiting Riemannian case are also recovered.