A class of solutions of Einstein's equations for the interior of a rigidly rotating perfect fluid

A general class of solutions of Einstein's equations for the interior of a rigidly rotating axisymmetric perfect fluid is presented, which depends on an arbitrary function. To get solutions explicitly one has to calculate two integrals involving the arbitrary function. The equipressure surfaces of all solutions of the class are spheres or planes. A family of solutions, which depend on four arbitrary real constants, is calculated explicitly. The solution of the family, which is obtained if we assign a specific value to one of its parameters, and which was found before, is futher generalized with the addition of one more parameter.