Faster-than-light waves in relativistic plasma in a weak magnetic field

Using the kinetic theory, we consider the change of spectral properties of relativistic plasma when a weak external magnetic field is switched on. In the first approximation with respect to the field, faster-than-light cyclotron waves are absent. The longitudinal wave is transformed into the extraordinary wave in the region of small wave vectors, whose dimension is proportional to the square root of the cyclotron frequency. The dispersion of the ordinary wave in relativistic plasma at finite temperature in a weak field does not differ from the dispersion of the transverse wave in an unmagnetized plasma. The dispersion of the extraordinary wave is determined from a quadratic equation with respect to the square of the frequency of the wave.