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Self-dual metrics in Husain's approach

M Jakimowicz and J Tafel

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We show that Husain's reduction of the self-dual Einstein equations is equivalent to the Plebański equation. The Bäcklund transformation between these equations is found. Contact symmetries of the Husain–Park equation and corresponding conservation laws are derived.


PACS

04.20.-q Classical general relativity

02.40.Tt Complex manifolds

02.40.Ky Riemannian geometries

MSC

83C20 Classes of solutions; algebraically special solutions, metrics with symmetries

83C05 Einstein's equations (general structure, canonical formalism, Cauchy problems)

83C40 Gravitational energy and conservation laws; groups of motions

32Qxx Complex manifolds

Subjects

Mathematical physics

Gravitation and cosmology

Dates

Issue 15 (7 August 2006)

Received 15 February 2006, in final form 1 June 2006

Published 11 July 2006



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