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Motion of charged particles in spacetimes with magnetic fields of spherical and hyperbolic symmetry | | Yen-Kheng Lim
; | | Date: |
1 Jun 2022 | | Abstract: | The motion of charged particles in spacetimes containing a submanifold of
constant positive or negative curvature are considered, with the
electromagnetic tensor proportional to the volume two-form form of the
submanifold. In the positive curvature case, this describes spherically
symmetric spacetimes with a magnetic monopole, while in the negative curvature
case, it is a hyperbolic spacetime with magnetic field uniform along hyperbolic
surfaces. Constants of motion are found by considering Poisson brackets defined
on a phase space with gauge-covariant momenta. In the spherically-symmetric
case, we find a correspondence between the trajectories on the Poincaré
cone with equatorial geodesics in a conical defect spacetime. In the hyperbolic
case, the analogue of the Poincaré cone is defined as a surface in an
auxiliary Minkowski spacetime. Explicit examples are solved for the Minkowski,
$mathrm{AdS}_4 imes S^2$, and the hyperbolic AdS-Reissner--Nordström
spacetimes. | | Source: | arXiv, 2206.00170 | | Services: | Forum | Review | PDF | Favorites | |
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