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arXiv · gr-qc/9707003

Lax pair tensors and integrable spacetimes

Kjell Rosquist·Martin Goliath
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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.

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Kjell Rosquist, Martin Goliath. 1997-07-02. Lax pair tensors and integrable spacetimes. https://doi.org/10.1023/a%3A1018817209424

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