Exact solutions for the Tikekar superdense star

Abstract

We analyze a relativistic model for superdense stars proposed by Tikekar [R. Tikekar, J. Math. Phys. 31, 2454 (1990)]. In this model the hypersurfaces generated by {t=const} have the geometry of the 3-spheroid which gives the solutions a clear geometrical characterization. The solution of the Einstein field equations is reduced to integrating a second order ordinary differential equation. New classes of solutions are presented by restricting the choice of the spheroidal parameter K so that polynomial solutions are admitted for the first solution and then we find that there exists another solution which is a product of polynomials and algebraic functions. A remarkable feature of the class of solutions generated is that they are expressible completely in terms of polynomials and algebraic functions. Some physical aspects of the solutions are briefly considered. We regain the Tikekar solution as a special case when K=−7. As another example we explicitly present the form of the solution when K=−2.