Relationships between the group-theoretic and soliton-theoretic techniques for generating stationary axisymmetric gravitational solutions

Journal Article · Mon Sep 01 04:00:00 EDT 1980 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.524680· OSTI ID:5014048

Cosgrove, C M

We investigate the precise interrelationships between several recently developed solution-generating techniques capable of generating asymptotically flat gravitational solutions with arbitrary multipole parameters. The transformations we study in detail here are the Lie groups Q and Q of Cosgrove, the Hoenselaers--Kinnersley--Xanthopoulos (HKX) transformations and their SL(2) tensor generalizations, the Neugebauer--Kramer discrete mapping, the Neugebauer Baecklund transformations I/sub 1/ and I/sub 2/, the Harrison Baecklund transformation, and the Belinsky--Zakharov (BZ) one- and two-soliton transformations. Two particular results, among many reported here, are that the BZ soliton transformations are essentially equivalent to Harrison transformations and that the generalized HKX transformation may be deduced as a confluent double soliton transformation. Explicit algebraic expressions are given for the transforms of the Kinnersley--Chitre generating functions under all of the above transformations. In less detail, we also study the Kinnersley--Chitre ..beta.. transformations, the non-null HKX transformations, and the Hilbert problems proposed independently by Belinsky and Zakharov, and Hauser and Ernst. In conclusion, we describe the nature of the exact solutions constructible in a finite number of steps with the available methods.

• Research Organization: Department of Physics, Montana State University, Bozeman, Montana 59717
• OSTI ID: 5014048
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 21:9; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

657003* -- Theoretical & Mathematical Physics-- Relativity & Gravitation
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ASYMPTOTIC SOLUTIONS
EQUATIONS
FIELD EQUATIONS
GRAVITATION
LIE GROUPS
MULTIPOLES
QUASI PARTICLES
SOLITONS
SYMMETRY GROUPS
TENSORS
TRANSFORMATIONS