Some new stationary axisymmetric asymptotically flat space-times obtained from Painlevé transcendents

For the stationary axisymmetric Einstein vacuum equations in cylindrical coordinates we find that both the Ernst equation and the two real equations which alternatively describe the stationary axisymmetric problem separate, leading to Painlevé transcendents. The boundary and asymptotic behaviors of the resulting space-times are investigated in both cases. Two families of solutions are determined which, away from the symmetry axis, become asymptotically flat. The analysis provides an example to the conjecture that the Painlevé property implies integrability.