On the Einstein-Weyl and conformal self-duality equations
Change log
Authors
Dunajski, M
Ferapontov, EV
Kruglikov, B
Abstract
The equations governing anti-self-dual and Einstein-Weyl conformal geometries can be regarded as `master dispersionless systems' in four and three dimensions respectively. Their integrability by twistor methods has been established by Penrose and Hitchin. In this note we present, in specially adapted coordinate systems, explicit forms of the corresponding equations and their Lax pairs. In particular, we demonstrate that any Lorentzian Einstein-Weyl structure is locally given by a solution to the Manakov-Santini system, and we find a system of two coupled third-order scalar PDEs for a general anti-self-dual conformal structure in neutral signature.
Description
Keywords
nlin.SI, nlin.SI, gr-qc, hep-th, math.DG
Journal Title
Journal of Mathematical Physics
Conference Name
Journal ISSN
0022-2488
1089-7658
1089-7658
Volume Title
56
Publisher
AIP Publishing
Publisher DOI
Sponsorship
Science and Technology Facilities Council (ST/J000434/1)
Science and Technology Facilities Council (ST/L000385/1)
Science and Technology Facilities Council (ST/L000385/1)