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We consider the self-force on a charged particle moving in a curved spacetimewith a background electromagnetic field, extending previous studies tosituations in which gravitational and electromagnetic perturbations arecomparable. The formal expression $f^{ret}_\alpha$ for the self-force on aparticle, written in terms of the retarded perturbed fields, is divergent, anda renormalization is needed to find the particle's acceleration at linear orderin its mass $m$ and charge $e$. We assume that, as in previous work in a Lorenzgauge, the renormalization for accelerated motion comprises an angle averageand mass renormalization. Using the short distance expansion of the perturbedelectromagnetic and gravitational fields, we show that the renormalization isequivalent to that obtained from a mode sum regularization in which onesubtracts from the expression for the self-force in terms of the retardedfields a singular part field comprising only the leading and subleading termsin the mode sum. The most striking part of our result, arising from aremarkable cancellation, is that the renormalization involves no mixing ofelectromagnetic and gravitational fields. In particular, the renormalized massis obtained by subtracting (1) the purely electromagnetic contribution from apoint charge moving along an accelerated trajectory and (2) the purelygravitational contribution from a point mass moving along the same trajectory.In a mode-sum regularization, the same cancellation implies that the requiredregularization parameters are sums of their purely electromagnetic andgravitational values.

Combined gravitational and electromagnetic self-force on charged particles in electrovac spacetimes