Variables separation in gravity

Details Variables separation in gravity Variables separation in gravity

2005-02-08

arxiv.org/abs/gr-qc/0502033v1

PoS WC2004 (2004) 027

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

8 pages. In proceedings of 4th International Winter Conference on Mathematical Methods in Physics (WC 2004), Rio de Janeiro, B

Scientific paper

To solve the problem of exact integration of the field equations or equations of motion of matter in curved spacetimes one can use a class of Riemannian metrics for which the simplest equations of motion can be integrated by the complete separation of variables method. Here, we consider the particular case of the class of Stackel metrics. These metrics admit integration of the Hamilton-Jacobi equation for test particle by the complete separation of variables method. It appears that the other important equations of motion (Klein-Gordon-Fock, Dirac, Weyl) in curved spacetimes can be integrated by complete separation of variables method only for the metrics, belonging to the class of Stackel spaces.

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