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arXiv · 2509.07052

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

Giulio Audagnotto·Antonino Di Piazza
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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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Giulio Audagnotto, Antonino Di Piazza. 2025-09-08. Exact solution of the DeWitt-Brehme-Hobbs equation in copropagating electromagnetic and gravitational waves. https://doi.org/10.1103/z4xf-rqcq

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