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The General Self-dual solution of the Einstein Equations

Sucheta Koshti·Naresh Dadhich
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Abstract

We obtain the most general explicit (anti)self-dual solution of the Einstein equations. We find that any (anti)self-dual solution can be characterised by three free functions of which one is harmonic. Any stationary (anti)self-dual solution can be characterised by a harmonic function. It turns out that the form of the Gibbons and Hawking multi-center metrics is the most general stationary (anti)self-dual solution. We further note that the stationary (anti)self-dual Einstein equations can be reinterpreted as the (anti)self-dual Maxwell equations on the Euclidean background metric.

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Sucheta Koshti, Naresh Dadhich. 1994-09-21. The General Self-dual solution of the Einstein Equations. https://arxiv.org/abs/gr-qc/9409046

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