1212.4456 (Javier E. Cuchí et al.)

An approximate global solution of Einstein's equation for a rotating
compact source with linear equation of state    [PDF]

Javier E. Cuchí, Antonio Gil-Rivero, Alfred Molina, Eduardo Ruiz

We use analytic perturbation theory to present a new approximate metric for a rigidly rotating perfect fluid source with equation of state (EOS) $\epsilon+(1-n)p=\epsilon_0$. This EOS includes the interesting cases of strange matter and Wahlquist's metric. It is fully matched to its approximate asymptotically flat exterior using Lichnerowicz junction conditions and it is shown to be a totally general matching using Darmois-Israel conditions and properties of the harmonic coordinates. Then we analyse the Petrov type of the interior metric and show, first, that in the case corresponding to Wahlquist's metric it can not be matched to the asymptotically flat exterior. Next, that this kind of interior can only be of Petrov types I, D or (in the static case) O and also that the non-static constant density case can only be of type I. Finally, we check that it can not be a source of Kerr's metric.

View original: http://arxiv.org/abs/1212.4456