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Lax pair tensors and integrable spacetimes | | Kjell Rosquist
; Martin Goliath
; | | Date: |
2 Jul 1997 | | Journal: | Gen.Rel.Grav. 30 (1998) 1521-1534 | | Subject: | General Relativity and Quantum Cosmology; Exactly Solvable and Integrable Systems | gr-qc nlin.SI solv-int | | Abstract: | The use of Lax pair tensors as a unifying framework for Killing tensors of arbitrary rank is discussed. Some properties of the tensorial Lax pair formulation are stated. A mechanical system with a well-known Lax representation -- the three-particle open Toda lattice -- is geometrized by a suitable canonical transformation. In this way the Toda lattice is realized as the geodesic system of a certain Riemannian geometry. By using different canonical transformations we obtain two inequivalent geometries which both represent the original system. Adding a timelike dimension gives four-dimensional spacetimes which admit two Killing vector fields and are completely integrable. | | Source: | arXiv, gr-qc/9707003 | | Services: | Forum | Review | PDF | Favorites | |
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