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20 January 2020
  » arxiv » gr-qc/9707003

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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
AbstractThe 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
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