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  • Letter
  • Open Access

Exact solution of the DeWitt-Brehme-Hobbs equation in copropagating electromagnetic and gravitational waves

Giulio Audagnotto1,2,3,* and Antonino Di Piazza2,4,†

  • *Contact author: giulio.audagnotto@unito.it
  • †Contact author: a.dipiazza@rochester.edu
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Phys. Rev. D 113, L061504 – Published 24 March, 2026

DOI: https://doi.org/10.1103/z4xf-rqcq

Abstract

An accelerated charge interacts with its own electromagnetic field, a phenomenon known as electromagnetic radiation reaction. The DeWitt-Brehme-Hobbs (DWBH) equation describes the motion of a charged mass in the presence of combined electromagnetic and gravitational fields, taking into account electromagnetic radiation-reaction effects. Here, we find the first exact analytical solution of the DWBH equation in the case of a charged mass in the presence of copropagating and otherwise arbitrary electromagnetic and gravitational plane waves. As a consequence of the Penrose limit, the scenario considered here can be seen as a local limit around ultrarelativistic trajectories in a general curved spacetime. Finally, the paradigmatic example of an electromagnetic wave in the presence of a constant-amplitude gravitational wave is worked out explicitly and it is shown how the presence of the gravitational wave can qualitatively change electromagnetic radiation-reaction effects.

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Phys. Rev. D 113, L061504– Published 24 March, 2026
  • Received 8 September 2025
  • Accepted 6 February 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Open access publication funded by the Max Planck Society.

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