abelian target space duals of gödel universe

We find new solutions for the field equations of bosonic string effective actionup to first order in α′ including the gödel spacetimes, axion field and dilaton.we then discuss in detail the abelian t-dualization of gödel spacetimes viathe poisson-lie (pl) t-duality approach. in this regards, it is found three dualmodels in such a way that dulizing is performed on the coordinates t, φ and zof the metric. the results of our study show that the abelian t-dual modelsare, under some of the special conditions, self-dual.