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The separation of the Hamilton-Jacobi equation for the Kerr metric

Published online by Cambridge University Press:  17 February 2009

G. E. Prince ,
J. E. Aldridge ,
S. E. Godfrey  and
G. B. Byrnes
G. E. Prince
Affiliation:
Department of Mathematics, La Trobe University, Bundoora, Victoria 3083, Australia.
J. E. Aldridge
Affiliation:
Department of Mathematics, La Trobe University, Bundoora, Victoria 3083, Australia.
S. E. Godfrey
Affiliation:
Department of Mathematics, La Trobe University, Bundoora, Victoria 3083, Australia.
G. B. Byrnes
Affiliation:
Department of Mathematics, La Trobe University, Bundoora, Victoria 3083, Australia.
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Abstract

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We discuss the separability of the Hamilton-Jacobi equation for the Kerr metric. We use a recent theorem which says that a completely integrable geodesic equation has a fully separable Hamilton-Jacobi equation if and only if the Lagrangian is a composite of the involutive first integrals. We also discuss the physical significance of Carter's fourth constant in terms of the symplectic reduction of the Schwarzschild metric via SO(3), showing that the Killing tensor quantity is the remnant of the square of angular momentum.

Type
Research Article
Information
The ANZIAM Journal , Volume 41 , Issue 2 , October 1999 , pp. 248 - 259
Copyright
Copyright © Australian Mathematical Society 1999

References

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