Abstract
In the present article, using the Lie group of transformations technique all the invariant solutions of Einstein’s field equations for non-conformally flat perfect fluid spheres of embedding class one have been derived by considering a 5-flat space. The same problem for conformally flat case was tackled by Thakadiyil and Jasim (Int. J. Theor. Phys. 52:3960, 2013) using the same technique but with the lesser number of symmetries and hence could obtain only lesser number of solutions as compared to the number of solutions in this paper. All the solutions thus obtained have been subjected to reality conditions. As far as the authors are aware some of the solutions are new.
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