From polarized gravitational waves to analytically solvable electromagnetic beams

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 analysed 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.

arXiv comment30 pages, 6 figures; final version to appear in PRD

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• Advances in QED with intense background fields
• The Weyl Double Copy for Gravitational Waves
• Classical Solutions and their Double Copy in Split Signature
• The classical double copy of non-singular black holes
• The Classical Double Copy of a Point Charge
• Asymptotic Weyl Double Copy
• On the Lagrangian formulation of the double copy to cubic order
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• Conformal symmetries and integrals of the motion in pp waves with external electromagnetic fields
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• Background ambiguity and the Gödel double copy
• Various disguises of the Pais-Uhlenbeck oscillator
• Revisiting the dynamics of a charged spinning body in curved spacetime
• NS-NS Spacetimes from Amplitudes
• Circularly polarized periodic gravitational wave and the Pais-Uhlenbeck oscillator