Radiation from perfect mirrors following prescribed relativistic trajectories

TL;DR

This paper analyzes the radiation emitted by perfect mirrors following specific relativistic paths, distinguishing between finite and infinite acceleration cases, and explores their connection to black hole analogs and radiation spectra.

Contribution

It provides a detailed calculation of radiation spectra for different mirror trajectories, clarifies the physicality of these models, and corrects previous derivations related to black body radiation.

Findings

Spectrum differs significantly between finite and infinite acceleration cases.

Infinite acceleration trajectory produces a black body radiation spectrum.

Previous derivations of black body spectrum in this context are corrected.

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.