Constants of motion for constrained Hamiltonian systems: A particle around a charged rotating black hole

Takahisa Igata, Tatsuhiko Koike, Hideki Ishihara

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Abstract

We discuss constants of motion of a particle under an external field in a curved spacetime, taking into account the Hamiltonian constraint, which arises from the reparametrization invariance of the particle orbit. As the necessary and sufficient condition for the existence of a constant of motion, we obtain a set of equations with a hierarchical structure, which is understood as a generalization of the Killing tensor equation. It is also a generalization of the conventional argument in that it includes the case when the conservation condition holds only on the constraint surface in the phase space. In that case, it is shown that the constant of motion is associated with a conformal Killing tensor. We apply the hierarchical equations and find constants of motion in the case of a charged particle in an electromagnetic field in black hole spacetimes. We also demonstrate that gravitational and electromagnetic fields exist in which a charged particle has a constant of motion associated with a conformal Killing tensor.

Original languageEnglish
Article number065027
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Volume83
Issue number6
DOIs
Publication statusPublished - 2011 Mar 25

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ASJC Scopus subject areas

  • Nuclear and High Energy Physics
  • Physics and Astronomy (miscellaneous)

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