Curved manifolds with conserved Runge-Lenz vectors
J.-P. Ngome
TL;DR
This paper uses van Holten's algorithm to identify conserved Runge-Lenz vectors on curved manifolds, specifically in generalized Taub-NUT and multi-center metrics, revealing new conserved quantities in these geometries.
Contribution
It introduces a method to find Runge-Lenz-type conserved quantities on curved manifolds, including the most general external potential for the generalized Taub-NUT metric.
Findings
Identified the most general external potential for conserved Runge-Lenz vectors in generalized Taub-NUT.
Discovered a conserved scalar Runge-Lenz-type quantity in two-center metrics.
Extended the understanding of conserved quantities in curved geometries.
Abstract
van Holten's algorithm is used to construct Runge-Lenz-type conserved quantities, induced by Killing tensors, on curved manifolds. For the generalized Taub-NUT metric, the most general external potential such that the combined system admits a conserved Runge-Lenz-type vector is found. In the multi-center case, the subclass of two-center metric exhibits a conserved Runge-Lenz-type scalar.
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