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arXiv · 2605.28663

First-Order Perturbations of Covariant Maxwell Equations in Gravitational Waves

Lingyue Lou·Haorong Wu·Xi-Long Fan
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Abstract

We present a systematic theoretical framework for investigating first-order electromagnetic (EM) perturbations induced by gravitational waves (GWs). Beginning with the covariant Maxwell equations, we derive the complete first-order perturbation equations in terms of both the EM field tensor and the four-potential, demonstrating their equivalence alongside the residual gauge invariance under the Lorenz gauge condition. Furthermore, explicit first-order expressions for the induced electric and magnetic fields, as well as the associated EM energy-momentum tensor, are obtained. As an explicit illustration, we analytically evaluate the interaction between a plane EM wave and a GW within the transverse-traceless gauge. By demonstrating that the maximum modulus of the coupling coefficient is on the order of $10^2$, we quantitatively establish that a typical astrophysical GW with a dimensionless strain of $h_0 \sim 10^{-21}$ generates a first-order EM response on the order of $10^{-19}$ relative to the incident field amplitude.

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Lingyue Lou, Haorong Wu, Xi-Long Fan. 2026-05-27. First-Order Perturbations of Covariant Maxwell Equations in Gravitational Waves. https://arxiv.org/abs/2605.28663

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