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

Takahisa Igata, Tatsuhiko Koike, Hideki Ishihara

研究成果: Article査読

16 被引用数 (Scopus)

抄録

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.

本文言語English
論文番号065027
ジャーナルPhysical Review D - Particles, Fields, Gravitation and Cosmology
83
6
DOI
出版ステータスPublished - 2011 3 25

ASJC Scopus subject areas

  • 核物理学および高エネルギー物理学
  • 物理学および天文学(その他)

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