MG11 
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Slowly rotating fluid balls of Petrov type D

The second order formalism by Hartle for slowly and rigidly rotating stars is used to study solutions where the equation of state is unspecified and the system instead is closed by requiring the interior solution to be of Petrov type D. The field equations for the interior are solved numerically using fourth order Runge-Kutta. The solutions are then matched to a second order axisymmetric vacuum solution, that includes the general asymptotically flat axisymmetric metric, using the Darmois-Israel procedure. The subset for which the solutions are asymptotically flat is determined. Properties like shape, equation of state and speed of sound are then determined for a number of solutions.