Cerenkov radiation in a Lorentz-violating and birefringent vacuum

We calculate the emission spectrum for vacuum Cerenkov radiation in Lorentz-violating extensions of electrodynamics. We develop an approach that works equally well in the presence or the absence of birefringence. In addition to confirming earlier work, we present the first calculation relevant to Cerenkov radiation in the presence of a birefringent photon $k_F$ term, calculating the lower-energy part of the spectrum for that case.

Figure 1

Possible shapes of the Mach cones corresponding to charges moving in two different directions. In one direction, two Mach cones are possible, but in another direction only one. In the leading-order approximation, the cones are right angled and circular, although the cones shown here are exaggeratedly narrow.

Figure 2

Polarization of the radiation on a single Mach cone in the birefringent $k_F$ theory. The cone is seen from above, with the charge moving out of the plane toward the viewer. The lines indicate the polarization direction of the radiation at various points on the cone’s surface, with their lengths denoting the relative intensities.