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Motion of charged particles in spacetimes with magnetic fields of spherical and hyperbolic symmetry
- Source :
- Phys. Rev. D vol.106, 064023 (2022)
- Publication Year :
- 2022
-
Abstract
- The motion of charged particles in spacetimes containing a submanifold of constant positive or negative curvature is 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 Poincar\'{e} cone with equatorial geodesics in a conical defect spacetime. In the hyperbolic case, the analogue of the Poincar\'{e} cone is defined as a surface in an auxiliary Minkowski spacetime. Explicit examples are solved for the Minkowski, $\mathrm{AdS}_4\times S^2$, and the hyperbolic AdS-Reissner--Nordstr\"{o}m spacetimes.<br />Comment: 34 pages, 8 figures. Typos corrected, Section 4 expanded thanks to the suggestion of the anonymous referee
- Subjects :
- General Relativity and Quantum Cosmology
High Energy Physics - Theory
Subjects
Details
- Database :
- arXiv
- Journal :
- Phys. Rev. D vol.106, 064023 (2022)
- Publication Type :
- Report
- Accession number :
- edsarx.2206.00170
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1103/PhysRevD.106.064023