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From polarized gravitational waves to analytically solvable electromagnetic beams

K. Andrzejewski* and S. Prencel

  • Department of Computer Science, Faculty of Physics and Applied Informatics, University of Lodz, Pomorska 149/153, 90-236, Lodz, Poland

  • *Corresponding author. k-andrzejewski@uni.lodz.pl
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Phys. Rev. D 100, 045006 – Published 8 August, 2019

DOI: https://doi.org/10.1103/PhysRevD.100.045006

Abstract

Using the correspondence between solutions of gravitational and gauge theories (the so-called classical double copy conjecture) some electromagnetic fields with vortices are constructed, for which the Lorentz force equations are analytically solvable. The starting point is a certain class of plane gravitational waves exhibiting the conformal symmetry. The notion of the Niederer transformation, crucial for the solvability, is analyzed in the case of the Lorentz force equation on the curved spacetimes as well as its derivation by means of integrals of motion (associated with conformal generators preserving these vortices) is presented. Furthermore, some models discussed recently in the context of the intense laser beams are constructed from their gravitational counterparts, with the special emphasis put on the focusing property, and new solvable examples are presented.

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Phys. Rev. D 100, 045006– Published 8 August, 2019
  • Received 29 January 2019
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