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arXiv · 1011.2479

General heavenly equation governs anti-self-dual gravity

A. A. Malykh·M. B. Sheftel
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Abstract

We show that the general heavenly equation, suggested recently by Doubrov and Ferapontov \cite{fer}, governs anti-self-dual (ASD) gravity. We derive ASD Ricci-flat vacuum metric governed by the general heavenly equation, null tetrad and basis of 1-forms for this metric. We present algebraic exact solutions of the general heavenly equation as a set of zeros of homogeneous polynomials in independent and dependent variables. A real solution is obtained for the case of neutral signature.

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A. A. Malykh, M. B. Sheftel. 2011-02-18. General heavenly equation governs anti-self-dual gravity. https://doi.org/10.1088/1751-8113/44/15/155201

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