Spectra for the Vacuum Cherenkov Effect in Astrophysical Electromagnetic Cascades with Lorentz Invariance Violation

Abstract: Lorentz invariance violation is a feature of several quantum gravity models in which Lorentz symmetry is broken at high energies, possibly leading to changes in particle behavior and interactions. In this work, we investigate vacuum Cherenkov radiation, a reaction in which an electron spontaneously emits a photon. This process, forbidden when Lorentz symmetry is unbroken, 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.