Geodesics of electrically and magnetically charged test particles in the Reissner-Nordström space-time: Analytical solutions

2010/11/24 by Saskia Grunau, Valeria Kagramanova · 125 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Charged particle #Classical mechanics #Cosmology and Gravitation Theories #Geodesic #Ion #Magnetic field #Magnetic monopole #Mathematical analysis #Mathematical physics #Mathematics #Motion (physics) #Noncommutative and Quantum Gravity Theories #Physics #Quantum mechanics #Space (punctuation) #Test particle #gr-qc

paper · pdf · doi:10.1103/physrevd.83.044009

published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 83(4) (American Physical Society)

arxiv created 2010/11/24 · openalex publication_date 2011/02/02 · arxiv updated 2011/02/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We present the full set of analytical solutions of the geodesic equations of charged test particles in the Reissner-Nordstr"om space-time in terms of the Weierstra\ss \ensuremath\wp, \ensuremathσ, and \ensuremathζ elliptic functions. Based on the study of the polynomials in the \ensuremathϑ and r equations, we characterize the motion of test particles and discuss their properties. The motion of charged test particles in the Reissner-Nordstr"om space-time is compared with the motion of neutral test particles in the field of a gravitomagnetic monopole. Electrically or magnetically charged particles in the Reissner-Nordstr"om space-time with magnetic or electric charges, respectively, move on cones similar to neutral test particles in the Taub-NUT space-times.

Citations

• Schwarzschild field inn dimensions and the dimensionality of space problem
• Complete Analytic Solution of the Geodesic Equation in Schwarzschild–(Anti-)de Sitter Spacetimes
• Classical monopoles: Newton, NUT space, gravomagnetic lensing, and atomic spectra
• Rotating, charged, and uniformly accelerating mass in general relativity
• A new look at the Plebanski-Demianski family of solutions

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• Innermost stable circular orbit of charged particles in Reissner-Nordström, Kerr-Newman, and Kerr-Sen spacetimes
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