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A Method for Generating New Solutions of Einstein's Equation. II
Abstract
A scheme is introduced which yields, beginning with any source-free solution of Einstein's equation with two commuting Killing fields for which a certain pair of constants vanish (e.g., the exterior field of a rotating star), a family of new exact solutions. To obtain a new solution, one must specify an arbitrary curve (up to parametrization) in a certain three-dimensional vector space. Thus, a single solution of Einstein's equation generates a family of new solutions involving two arbitrary functions of one variable. These transformations on exact solutions form a non-Abelian group. The extensive algebraic structure thereby induced on such solutions is studied.
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Citations
Cited by
Lidsey, J. E., Wands, D., & Copeland, E. J. (2000) · Physics Reports · doi:10.1016/s0370-1573(00)00064-8 · Cited by 480
Classification of Gravitational Instanton symmetries
Gibbons, G. W., & Hawking, S. W. (1979) · Communications in Mathematical Physics · doi:10.1007/bf01197189 · Cited by 467
Reduction of Einstein’s equations for vacuum space-times with spacelike U(1) isometry groups
Moncrief, V. (1986) · Annals of Physics · doi:10.1016/s0003-4916(86)80009-4 · Cited by 124
Canonical quantum supergravity in three dimensions
Matschull, H.-J., & Nicolai, H. (1994) · Nuclear Physics B · doi:10.1016/0550-3213(94)90464-2 · Cited by 28
Metadata
- Authors
- Geroch, R.
- Venue
- Journal of Mathematical Physics
- Publisher
- AIP Publishing
- Published
- 1972-03-01
- Volume
- 13
- Issue
- 3
- Pages
- 394-404
- ISSN
- 0022-2488 (ISSN-L)
- 1089-7658
- OpenAlex
- W2010255817
- Cited by
- 431
- References
- 0
- FWCI
- 2.65
- Type
- journal article
- Language
- en
- Open access
- closed
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- Geroch, R. (1972). A Method for Generating New Solutions of Einstein's Equation. II. Journal of Mathematical Physics. https://doi.org/10.1063/1.1665990
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