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Motion of charged particles in spacetimes with magnetic fields of spherical and hyperbolic symmetry  YenKheng 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 twoform 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 gaugecovariant momenta. In the sphericallysymmetric
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 AdSReissnerNordström
spacetimes.  Source:  arXiv, 2206.00170  Services:  Forum  Review  PDF  Favorites 


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