General heavenly equation governs anti-self-dual gravity
Mathematical Physics
2013-06-11 v3 General Relativity and Quantum Cosmology
math.MP
Exactly Solvable and Integrable Systems
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.
Keywords
Cite
@article{arxiv.1011.2479,
title = {General heavenly equation governs anti-self-dual gravity},
author = {A. A. Malykh and M. B. Sheftel},
journal= {arXiv preprint arXiv:1011.2479},
year = {2013}
}
Comments
LaTeX2e, 17 pages. Important additions and corrections made. A new section added on derivation of Lax pair