Gödel Type solution with rotation, expansion and closed time-like curves

Abstract

We propose a time-varying parameter $\underlineα$ for Gödel 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, Gödel and steady state properties are obtained.