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In isotropic but Lorentz- and CPT-violating electrodynamics, it is known thata charge in unifom motion does not lose any energy to Cerenkov radiation. Thispresents a puzzle, since the radiation appears to be kinematically allowed formany modes. Studying the Fourier transforms of the most important terms in themodified magnetic field and Poynting vector, we confirm the vanishing of thethe radiation rate. Moreover, we show that the Fourier transform of the fieldchanges sign between small and large wave numbers. This enables modes with verylong wavelengths to carry negative energies, which cancel out the positiveenergies carried away by modes with shorter wavelengths. This cancelation hadpreviously been inferred but never explicitly demonstrated.

Mode Analysis for Energetics of a Moving Charge In Lorentz- and CPT-Violating Electrodynamics