Radiation from perfect mirrors following prescribed relativistic trajectories

Abstract

The question is examined of a mirror which starts from rest and either (i) accelerates for some time and eventually reverts to motion at constant velocity, or (ii) continues accelerating forever. A sharp distinction is made between cases (i) and (ii) concerning the spectrum of the emitted radiation, and the qualitative difference between the two cases is pointed out. The Bogolubov coefficients are calculated for a trajectory of type (i). A type (ii) trajectory is entirely unphysical as far as any realistic mirror is concerned, however it is of interest in that it has been used as a simple analog of black hole collapse. The spectrum emitted for the type (ii) trajectory z=-ln(cosht) is examined and it is shown that it is indeed that of a black body. Inconsistencies in previous derivations of the above result are pointed out.