Lax Pair Tensors and Integrable Spacetimes |
| |
Authors: | Kjell Rosquist Martin Goliath |
| |
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. |
| |
Keywords: | TODA LATTICE KILLING TENSOR |
本文献已被 SpringerLink 等数据库收录! |