Note on stationary axisymmetric vacuum spacetimes with inside ellipsoidalsymmetry,

Rácz, István (1992) Note on stationary axisymmetric vacuum spacetimes with inside ellipsoidalsymmetry,. CLASSICAL AND QUANTUM GRAVITY, 9 (8). L93-L98. ISSN 0264-9381

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Abstract

We consider stationary-axisymmetric vacuum spacetimes possessing an additional `inside' symmetry property; namely we assume that the projected Riemannian 3-space induced by the stationary Killing field can be filled in with a one-parameter congruence of confocal ellipsoids. We present a family of exact solutions of vacuum Einstein's equations possessing these symmetries, and it is shown that these spacetimes consist of a three-parameter family of solutions which coincide with the subfamily of the Kerr-NUT spacetimes with vanishing electric (and magnetic) charge. Hence, a simple geometrical characterization can be given for this subfamily of algebraically specialized Petrov type D solutions which resulted by the application of completely different spin coefficient techniques.

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