Javier E. Cuchí, Jesús Martín, Alfred Molina, Eduardo Ruiz
We compare an approximation of Wahlquist's exact solution with a stationary and axisymmetric metric for a rigidly rotating perfect fluid with the equation of state $\mu + 3p= \mu_0$, a sub-case of a global approximate metric obtained recently for some of us. This comparison allows us in particular to determine the approximate relation between the rotation velocity of the fluid and the $r_0$ parameter of Wahlquist's metric. Through some coordinate changes we manage to make every component of both approximate metrics equal. In this situation, the free constants of our metric take the values needed for it to be of Petrov type D. These values do not allow matching with an asymptotically flat vacuum exterior.
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http://arxiv.org/abs/1301.4962
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