Talk abstract details

We construct an approximate asymptotically flat stationary and axisymmetric vacuum metric by imposing matching conditions on an interior metric associated to a perfect fluid with the equation of state $\mu+(1-n)p=\mu_0$. We also discuss the dependence of the multipole moments on the parameters of the source. Finally we recover, in the newtonian limit for a perfect fluid with constant mass density, the same results as in the classic case of the Mac Laurin ellipsoids.