Cosgrove, Christopher M. (1981) Bäcklund transformations in the Hauser–Ernst formalism for stationary axisymmetric spacetimes. Journal of Mathematical Physics, 22 (11). pp. 2624-2639. ISSN 0022-2488. http://resolver.caltech.edu/CaltechAUTHORS:COSjmp81
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It is shown that Harrison's Bäcklund transformation for the Ernst equation of general relativity is a two-parameter subset (not subgroup) of the infinite-dimensional Geroch group K. We exhibit the specific matrix u(t) appearing in the Hauser–Ernst representation of K for vacuum spacetimes which gives the Harrison transformation. Harrison transformations are found to be associated with quadratic branch points of u(t) in the complex t plane. The coalescence of two such branch points to form a simple pole exhibits in a simple way the known factorization of the (null generalized) HKX transformation into two Harrison transformations. We also show how finite (i.e., already exponentiated) transformations in the B group and nonnull groups of Kinnersley and Chitre can be constructed out of Harrison and/or HKX transformations. Similar considerations can be applied to electrovac spacetimes to provide hitherto unknown Bäcklund transformations. As an example, we construct a six-parameter transformation which reduces to the double Harrison transformation when restricted to vacuum and which generates Kerr–Newman–NUT space from flat space.
|Additional Information:||Copyright © 1981 American Institute of Physics. (Received 30 March 1981; accepted for publication 26 June 1981) This research has benefited from discussions with William Kinnersley and Terry Lemley. I also wish to thank Isidore Hauser and Frederick J. Ernst for making their results available prior to publication. Supported in part by the National Science Foundation (AST79-22012). [C.M.C. was a] Richard Chase Tolman Research Fellow.|
|Subject Keywords:||GENERAL RELATIVITY THEORY, TRANSFORMATIONS, SYMMETRY GROUPS, SPACE−TIME, GRAVITATIONAL FIELDS, METRICS|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Archive Administrator|
|Deposited On:||04 Jun 2008|
|Last Modified:||26 Dec 2012 10:04|
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