Spectra for reactions in astrophysical electromagnetic cascades with Lorentz invariance violation: The vacuum Cherenkov effect

Lorentz invariance violation is a feature of several quantum gravity models in which Lorentz symmetry is broken at high energies, leading to potential changes in particle behavior and interactions. In this study, we investigate vacuum Cherenkov radiation, a reaction in which an electron spontaneously emits a photon. This process, forbidden when considering unbroken Lorentz symmetry, is a phenomenological consequence of some quantum gravity models. We derive, for the first time, the spectra for the vacuum Cherenkov reaction, and confirm our results numerically. These results can be used to derive limits on Lorentz invariance violation.