On the vacuum Cherenkov radiation in noncommutative electrodynamics and the elusive effects of Lorentz violation

We show that in the framework of noncommutative classical electrodynamics Cherenkov radiation is permitted in vacuum and we explicitly compute its spectrum at first order in the noncommutative parameter. We discuss the phenomenological impact of the merge of this new analysis with the old results of the substantial modi. cation to the spectrum of the synchrotron radiation obtained in Castorina P., Iorio A. and Zappala D., Phys. Rev. D, 69 ( 2004) 065008. We propose to consider the pulsars' radiation spectrum - due to its very strong magnetic field - to investigate these Lorentz violating effects in astrophysical phenomena.