G\"{o}del Type solution with rotation, expansion and closed time-like curves

TL;DR

This paper introduces a dynamic G"odel metric with time-varying parameters, leading to a universe model exhibiting rotation, expansion, and closed time-like curves, blending features of standard, G"odel, and steady state cosmologies.

Contribution

It presents a novel G"odel-type solution with time-dependent parameters and an associated energy-momentum tensor, incorporating expansion, rotation, and closed time-like curves.

Findings

Derivation of Einstein's equations for the evolving G"odel universe

Introduction of a time-varying gravitational and cosmological term

Model exhibits rotation, expansion, and closed time-like curves

Abstract

We propose a time-varying parameter $\underline{\alpha}$ for G\"{o}del metric and an energy momentum tensor corresponding to this geometry is found. To satisfy covariance arguments time-varying gravitational and cosmological term are introduced. The ``Einstein's equation'' for this special evolution for the Universe are written down where expansion, rotation and closed time-like curves appear as a combination between standard model, G\"{o}del and steady state properties are obtained.