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

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.

Figures (1)

• Figure 1: The function $R(\varphi, \lambda) = \frac{(w(\varphi) - 1)_{\lambda}}{(w(\varphi) - 1)_{\lambda = 0 } }$ for $a^i(\phi) = -\delta^i{}_1 a_0 \cos(\omega\phi)$ and different values of $\lambda$. The black dashed line at 9/4 represents the asymptote of $R(\varphi, 1)$.