The General Self-dual solution of the Einstein Equations

Details The General Self-dual solution of the Einstein Equations The General Self-dual solution of the Einstein Equations

1994-09-21

arxiv.org/abs/gr-qc/9409046v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

14 Pages, Latex, IUCAA 94/29

Scientific paper

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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