Interior Solutions to the Solutions of Schwarzschild and Kerr
Second Edition
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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 Schwarzschild 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 Schwarzschild are presented. The values of their parameters for...
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 Schwarzschild 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 Schwarzschild are presented. The values of their parameters for which the Weak Energy Conditions 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 relations for which the Darmois and the Lichnerowicz matching conditions are satisfied. The solutions should be regular and should satisfy certain energy conditions. We present several solutions which howeverdo not satisfy both requirements. Also we present regular interior solutions to the solution of Kerr which satisfy the Weak and the Strong Energy Conditions.
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