Double shell stars as source of the Kerr metric in the CMMR approximation

Cuchí, J. E., Molina, A., Ruiz, E.

The Cabezas, Martín, Molina and Ruiz (CMMR) method allows us to build global analytic solutions of Einstein's equations for stationary isolated and rigidly rotating perfect fluid solutions. We start from a double approximation: Postminkowskian and slow rotation, and end up getting a matched global solution from the inner and outer metrics. The metrics this way obtained have some uses. In particular, we will show the application of the scheme to the equation of state $mu+(1-n)p=mu_0$ and how it can be applied to a build a source with two concentric comoving shells of fluid with different $mu_0$. We will also analyse the conditions under which this configuration can be a source of the Kerr metric.