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Abstract

Killing Tensors and Conserved Quantities of a Relativistic Pariticle in External Fields

We discuss geometrical properties of a spacetime which admits constants of motion for a relativistic particle, which is a constrainted system because of the reparametrization invariance, moving in external fields. We formulate hierarchical equations which are the condition for the existence of the conserved quantities. These are interpreted as a generalization of the Killing equation to the particle systems in the external fields. We apply it to charged particle systems as a specific case, and we show explicit forms of the conserved quantities of a charged particle moving in four- and five-dimensional charged black holes by solving the hierarchical equations.

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