Perlick's classification of (3 + 1)-dimensional spherically symmetric and static spacetimes (M, eta = -1/v dt(2) + g) for which the classical Bertrand theorem holds (Perlick V 1992 Class. Quantum Grav. 9 1009) is revisited. For any Bertrand spacetime (M, eta) the term V (r) is proven to be either the intrinsic Kepler-Coulomb or the harmonic oscillator potential on its associated Riemannian 3-manifold (M, g). Among the latter 3-spaces (M, g) we explicitly identify the three classical Riemannian spaces of constant curvature, a generalization of a Darboux space and the Iwai-Katayama spaces generalizing the MIC-Kepler and Taub-NUT problems. The key dynamical role played by the Kepler and oscillator potentials in Euclidean space is thus extended to a wide class of three-dimensional curved spaces.

Ballesteros, A., Enciso, A., Herranz, F.j., Ragnisco, O. (2008). Bertrand spacetimes as Kepler/oscillator potentials RID B-5702-2011 RID F-2453-2010. CLASSICAL AND QUANTUM GRAVITY, 25(16) [10.1088/0264-9381/25/16/165005].

Bertrand spacetimes as Kepler/oscillator potentials RID B-5702-2011 RID F-2453-2010

RAGNISCO, Orlando
2008-01-01

Abstract

Perlick's classification of (3 + 1)-dimensional spherically symmetric and static spacetimes (M, eta = -1/v dt(2) + g) for which the classical Bertrand theorem holds (Perlick V 1992 Class. Quantum Grav. 9 1009) is revisited. For any Bertrand spacetime (M, eta) the term V (r) is proven to be either the intrinsic Kepler-Coulomb or the harmonic oscillator potential on its associated Riemannian 3-manifold (M, g). Among the latter 3-spaces (M, g) we explicitly identify the three classical Riemannian spaces of constant curvature, a generalization of a Darboux space and the Iwai-Katayama spaces generalizing the MIC-Kepler and Taub-NUT problems. The key dynamical role played by the Kepler and oscillator potentials in Euclidean space is thus extended to a wide class of three-dimensional curved spaces.
2008
Ballesteros, A., Enciso, A., Herranz, F.j., Ragnisco, O. (2008). Bertrand spacetimes as Kepler/oscillator potentials RID B-5702-2011 RID F-2453-2010. CLASSICAL AND QUANTUM GRAVITY, 25(16) [10.1088/0264-9381/25/16/165005].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/117840
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