General heavenly equation governs anti-self-dual gravity

Details General heavenly equation governs anti-self-dual gravity General heavenly equation governs anti-self-dual gravity

2010-11-10

arxiv.org/abs/1011.2479v3

J.Phys.A44:155201,2011

Physics

Mathematical Physics

LaTeX2e, 17 pages. Important additions and corrections made. A new section added on derivation of Lax pair

Scientific paper

10.1088/1751-8113/44/15/155201

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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