An infinite hierarchy of conservation laws and nonlinear superposition principles for self-dual Einstein spaces
- 1 February 1985
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 26 (2) , 229-234
- https://doi.org/10.1063/1.526652
Abstract
Self-dual Einstein spaces are shown to admit an infinite hierarchy of conservation laws, and this hierarchy is then used to derive a formal version of Penrose’s twistor construction. The set of formal holomorphic bundles of fiber dimension 2 over the Riemann sphere P1 is shown to form a formal infinite group which is used to derive nonlinear superposition principles. As an example of our methods a new self-dual Einstein space is obtained as the result of a ‘‘collision’’ of complex pp-waves ‘‘traveling in opposite directions.’’Keywords
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