EXACT-SOLUTIONS FOR THE TIKEKAR SUPERDENSE STAR

We analyze a relativistic model for superdense stars proposed by Tikek ar [R. Tikekar, J. Math. Phys. 31, 2454 (1990)]. In this model the hyp ersurfaces generated by {t = const} have the geometry of the 3-spheroi d which gives the solutions a clear geometrical characterization. The solution of the Einstein field equations is reduced to integrating a s econd order ordinary differential equation. New classes of solutions a re presented by restricting the choice of the spheroidal parameter K s o that polynomial solutions are admitted for the first solution and th en we find that there exists another solution which is a product of po lynomials and algebraic functions. A remarkable feature of the class o f 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. (C) 1996 American Institute of Phys ics.