Solutions in Self-Dual Gravity Constructed Via Chiral Equations

Abstract

The chiral model for self-dual gravity given by Husain in the context of the chiral equations approach is discussed. A Lie algebra corresponding to a finite dimensional subgroup of the group of symplectic diffeomorphisms is found, and then use for expanding the Lie algebra valued connections associated with the chiral model. The self-dual metric can be explicitly given in terms of harmonic maps and in terms of a basis of this subalgebra.

Plain Latex, 13 Pages, major revisions of style in the above proof, several Comments added. Version to appear in Physical Review D

References in corpus (4)

• Self-dual gravity as a two dimensional theory and conservation laws
• Self-dual gravity and the chiral model
• On Self-Dual Gravity I
• Axisymmetric Stationary Solutions as Harmonic Maps

Cited by in corpus (2)

• Further Remarks on the Chiral Model Approach to Self-Dual Gravity
• Discrete and Continuous Bogomolny Equations through the Deformed Algebra