Accelerated charges emit both electromagnetic and gravitational radiation.
    Classically, it was found that the electromagnetic energy spectrum radiated by
    an electron in a monochromatic plane wave is proportional to the corresponding
    gravitational one. Quantum mechanically, it was shown that the amplitudes of
    graviton photoproduction and Compton scattering are proportional to each other
    at tree level. Here, by combining strong-field QED and quantum gravity, we
    demonstrate that the amplitude of nonlinear graviton photoproduction in an
    arbitrary plane wave is proportional to the corresponding amplitude of
    nonlinear Compton scattering. Also, introducing classical amplitudes we prove
    that the proportionality relies on the semiclassical nature of the electron’s
    motion in a plane wave and on energy-momentum conservation laws, leading to the
    same proportionality constant in the classical and quantum case. These results
    deepen the intertwine between gravity and electromagnetism into both a
    nonlinear and a quantum level.

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