Structure of the Tomimatsu--Sato gravitational field

The new Tomimatsu-Sato solution is a stationary axisymmetric vacuum solution of the gravitational field equations which has been proposed as a possible external field for rotating stellar objects. The solution is a Petrov type-I rotating generalization of a static Weyl solution. It has the unusual feature of a naked singularity outside a Killing horizon. In this note, after the asymptotic flatness of the solution is demonstrated, the energy and angular momentum are calculated and found to be $m$ and $ma$, respectively. The locations of the horizons, infinite red-shift surfaces, curvature singularities, and closed timelike lines are given. The Killing horizon is found to be nonregular, and thus cannot be identified as an event horizon, contrary to the claim of Tomimatsu and Sato.