P V Pryse 1993 Class. Quantum Grav. 10 163 doi:10.1088/0264-9381/10/1/016
Group invariant solutions of the Ernst equation
P V Pryse
Show affiliationsSeveral implicit solutions of the Ernst equation are derived by use of its five-parameter local symmetry group. One of these solutions is a generalization of an implicit solution found by Leaute and Marchilacy (1979) and one is a generalization of an explicit solution found by Kaliappan and Lakshaman (1981). Except for the generalization of the Kaliappan and Lakshaman solution, each of these solutions is given in terms of a function defined as a solution of a second-order, non-linear, ordinary differential equation. One of these ordinary differential equations is integrated by quadratures by use of its own two-parameter local symmetry group, the result being three explicit solutions of the Ernst equation. These explicit solutions belong to a class found by Cosgrove (1978) that are defined in terms of a solution of an ordinary differential equation. For one of these explicit solutions the metric of the spacetime manifold is constructed. This solution is not asymptotically flat.
- PACS
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02.30.Hq Ordinary differential equations
- MSC
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58D17 Manifolds of metrics (esp. Riemannian)
- Subjects
- Dates
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Issue 1 (January 1993)
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Group invariant solutions of the Ernst equation
P V Pryse 1993 Class. Quantum Grav. 10 163
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