Electrodynamics of hyperbolically accelerated charges II. Does a charged particle with hyperbolic motion radiate?

The question whether a hyperbolically moving charge emits radiation is discussed. In order to arrive at an unambiguous answer the question is considered from several points of view. The power spectrum of the electromagnetic field due to a hyperbolically moving charge is deduced. Also we analyse the field in order to clarify whether it contains a radiation zone. Our conclusion is that a charge with constant proper acceleration emits radiation in spite of the fact that the Poynting vector of the field vanishes everywhere in the instantaneous inertial rest frame of the charge