Maxwell equations in a spherically symmetric black-hole background and radiation by a radially moving charge

Abstract

The possibil i ty of observation of black holes, if they exist, rests mainly in the detection of radiat ion, gravi ta t ional or electromagnetic, produced by charged or neutral ma t te r moving in i ts vicinity. Mechanisms for radiat ion during mat ter accretion (1) or in moving plasma (2) have been proposed and examined. These problems arc of vast complexi ty and presently can be analysed only with very crude approximations. Thus i t is worth-while to consider problems which can be solved exactly, even if they correspond to very idealized situations. Experience with solution of these problems may be of help for future analysis of more complex situations as i t brings an insight into the basic features of the laws of physics involved. Thus the emission of gravi tat ional radiation by a point part icle near a Schwarzschild black hole has received much at tent ion la te ly (3). Also the electromagnetic radiat ion of a point part icle in circular orbits has been calculated (3.4) using the method outlined by ~RuFFINI, TIOMNO and VISHVESHWARA (5). Another interesting problem is tha t of the radiat ion emit ted by a point charge q, with mass me, moving radia l ly in a Reissner-Nordstr6m black-hole background. A previous a t t empt to solve this problem by numerical integration of the equations resulting direct ly from those of I (ref. (5)) was never completed (~). Contrary to the case of circular orbits (4) (bound orbits), the integrat ion of the equation (eq. (I-13))