Solution generating technique for the Einstein equations
Thesis/Dissertation
·
OSTI ID:5403706
During the last 20 years, since R. Kerr found the first rotating solution and F.J. Ernst devised a simple form of the gravitational field equations for rotating bodies, there has been much progress in this area. On the one hand, Tomimatsu and Sato developed an infinite sequence of two parameter exact solutions, while Plebanski and Demianski found the general solution of Petrov type D. On the other hand, after 1977, solution-generating techniques were developed very rapidly, e.g., the Kinnersley-Chitre (K-C) transformations, Harrison's Backlund transformations, and the latest generating technique, the homogeneous Hilbert problem (HHP) formulated by Hauser and Ernst. On the basis of the HHP, the author shows in this dissertation how to use various transformations to generate famous known solutions as well as new solutions. Some of the new results, such as an N = 2 Cosgrove solution and a nine-parameter solution worked out by the author and colleagues, are described in detail. The main part of this dissertation concerns the treatment of a large class of K-C transformations (polynomial transformations), both in the vacuum and the electrovac case, encompassing many well-known transformations. By using the polynomial transformations, the author generates without iteration a many-parameter solution for the vacuum which is a natural generalization of the N-fold Neugebauer solution, and a many-parameter solution for the electrovac which is a natural generalization of the N-fold Cosgrove solution.
- Research Organization:
- Illinois Inst. of Tech., Chicago (USA)
- OSTI ID:
- 5403706
- Country of Publication:
- United States
- Language:
- English
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