Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2010-05-11
Phys.Rev.D83:065027,2011
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
20 pages
Scientific paper
10.1103/PhysRevD.83.065027
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 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 electro-magnetic field in black hole spacetimes. We also demonstrate that gravitational and electro-magnetic fields exist in which a charged particle has a constant of motion associated with a conformal Killing tensor.
Igata Takahisa
Ishihara Hideki
Koike Tatsuhiko
No associations
LandOfFree
Constants of Motion for Constrained Hamiltonian Systems: A Particle around a Charged Rotating Black Hole does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Constants of Motion for Constrained Hamiltonian Systems: A Particle around a Charged Rotating Black Hole, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Constants of Motion for Constrained Hamiltonian Systems: A Particle around a Charged Rotating Black Hole will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-384572