Hostname: page-component-848d4c4894-pjpqr Total loading time: 0 Render date: 2024-06-20T13:05:21.441Z Has data issue: false hasContentIssue false

Applications of symmetry groups and the Wahlquist-Estabrook procedure in general relativity

Published online by Cambridge University Press:  17 April 2009

Phillip Charles Harmsworth
Affiliation:
Department of Applied Mathematics, University of Sydney, New South Wales, Australia. 2006
Rights & Permissions [Opens in a new window]

Abstract

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Abstracts of Australasian of PhD theses
Copyright
Copyright © Australian Mathematical Society 1988

References

[1]Cosgrove, C.M., ‘A new formulation of the field equations for the stationary axisymmetric vacuum gravitational field I. General theory’, J.Phys. A:Math. Gen 11 (1978a), 23892404.CrossRefGoogle Scholar
[2]Cosgrove, C.M., ‘A new formulation of the field equations for the stationary axisymmetric gravitational field II. Separable solutions’, J. Phys. A:Math. Gen 11 (1978b), 24052430.CrossRefGoogle Scholar
[3]Cosgrove, C.M., ‘Stationary axisymmetric gravitational fields: an asymptotic flatness preserving transformation’, in Proc. Einstein Centenary Summer School, Perth W.A. 124: Lecture Notes in Physics, Edited by Edwards, C., 223101, 1979 (Springer, 1980).Google Scholar
[4]Dodd, R.K. and Fordy, A., ‘The prolongation structures of quasi-polynomial flows’, Proc. Roy. Soc. Lond. Ser A 385 (1983), 389429.Google Scholar
[5]Ernst, F.J., ‘New formulation of the axially symmetric gravitational field problem’, Phys. Rev. 167 (1968), 11751178.CrossRefGoogle Scholar
[6]Estabrook, F.B. and Wahlquist, H.D., ‘Prolongation structures of nonlinear evolution equations II’, J. Math. Phys. 17 (1976), 12931297.CrossRefGoogle Scholar
[7]Harrison, B.K., ‘Unification of Ernst-equation Bäcklund transformations using a modified Wahlquist-Estabrook technique’, J. Math. Phys. 24 (1983), 21782187.CrossRefGoogle Scholar
[8]Hermann, R., ‘Pseudopotentials of Estabrook and Wahlquist, the geometry of solitons and the theory of connections’, Phys. Rev. Lett. 37 (1976), 835836.CrossRefGoogle Scholar
[9]Neugebauer, G., ‘Bäcklund transformations of axially symmetric gravitational fields’, J. Phys. A: Math. Gen. 12 (1979), L67L70.CrossRefGoogle Scholar
[10]Wahlquist, H.D. and Estabrook, F.B., ‘Prolongation structures of nonlinear evolution equations’, J. Maths. Phys. 18 (1975), 17.CrossRefGoogle Scholar