Matter collineations of Spacetime Homogeneous G\"odel-type Metrics

TL;DR

This paper investigates matter collineations in spacetime homogeneous G"odel-type metrics, revealing infinite collineations in degenerate cases and new parameter constraints affecting causality features.

Contribution

It provides a detailed analysis of matter collineations in G"odel-type spacetimes, highlighting differences between degenerate and non-degenerate cases and their implications.

Findings

Infinite matter collineations in degenerate case

No proper matter collineations in non-degenerate case

New constraints on parameters affecting causality

Abstract

The spacetime homogeneous G\"odel-type spacetimes which have four classes of metrics are studied according to their matter collineations. The obtained results are compared with Killing vectors and Ricci collineations. It is found that these spacetimes have infinite number of matter collineations in degenerate case, i.e. det$(T_{ab}) = 0$, and do not admit proper matter collineations in non-degenerate case, i.e. det$(T_{ab}) \ne 0$. The degenerate case has the new constraints on the parameters $m$ and $w$ which characterize the causality features of the G\"odel-type spacetimes.