Interior Solutions to the Solution of Schwarzschild and to the Solution of Kerr (Paperback)

We present a big number of solutions which are interior solutions to the solution of Schwarzschild or to the solution of Kerr. The parameters of all interior solutions to the solution of Schwarzchild are chosen such that in the interior region the solutions are regular. The metric of the solutions which match to the solution of Schwarzschild depends on two functions f (r) and h(r) . Seven families of them, for which f (r) = (h(r)) *2 and six other families are given. Also several perfect fluid solutions interior to the solution of Schwarzchild are presented. The values of their parameters for which the Weak Energy Conditions (WEC) are satisfied are found. The metric of the solutions which match to the solution of Kerr depends on two functions F (r) and H(r), which satisfy certain matching conditions. We find interior solutions with F (r) =r *2, which satisfy the WEC but have the ring singularity of Kerr. Also we present a regular solution with F (r) = r *2, which however does not satisfy the WEC in the whole interior region. The case with F (r) not equal to r *2 is examined and we find regular interior solutions which do not satisfy the WEC in the whole interior region.