Geodesic Synchrotron Radiation

This paper presents the results and methods of computing the high-frequency radiation emitted by freely falling particles moving in circular geodesic orbits in a spherically symmetric gravitational field. The high-frequency radiation, to which the methods of this paper apply, is the principal part of radiated energy only in the case of a particle moving in a highly relativistic, and therefore unstable, circular geodesic. The geodesic synchrotron radiation emitted in this case shows as main features excitation of high-frequency harmonics and a narrow angular distribution. A Green's-function solution of the scalar wave equation is obtained using WKB methods. For application to relativistic circular orbits a parabolic WKB approximation is required and yields solutions in terms of parabolic cylinder functions. Although only scalar radiation is treated explicitly in this paper, the Green's functions constructed here for the solution of the scalar wave equation also suffice for the vector and tensor calculations.