A family of heavenly metrics

Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology

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Scientific paper

Non-invariant solutions of the Boyer-Finley equation determine exact solutions of the Einstein field equations with only one rotational Killing vector. For the case of Euclidean signature such a metric was constructed by Calderbank and Tod. Recently Martina, Sheftel and Winternitz applied the method of group foliation to the Boyer-Finley equation and reproduced the Calderbank-Tod solution together with new solutions. We point out that in the case of ultra-hyperbolic signature there exist three inequivalent forms of metric. Only one of these can be obtained by analytic continuation from the Calderbank-Tod solution whereas the other two are new.

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