Geodesic synchrotron radiation in the Kerr geometry by the method of asymptotically factorized Green's functions

Abstract

The scalar, electromagnetic, and gravitational geodesic synchrotron radiation (GSR) spectra are determined for the case of a test particle moving on a highly relativistic circular orbit about a rotating (Kerr) black hole. One finds that the spectral shape depends only weakly on the angular momentum parameter $\frac{a}{M}$ of the black hole, but the total radiated power drops unexpectedly for $\frac{a}{M}\ensuremath{\gtrsim}0.95$ and vanishes for $\frac{a}{M}\ensuremath{\rightarrow}1$. A spin-dependent factor (involving the inner product of the polarization of a radiated quantum with the source) is isolated to explain the dependence of the spectral shape upon the spin of the radiated field. Although the scalar wave equation is solved by separation of variables, this procedure is avoided for the vector and tensor cases by postulating there a sum-over-states expansion for the Green's function similar to that found to hold in the scalar case. The terms in this sum, significant for GSR, can then be evaluated in the geometric optics approximation without requiring the use of vector or tensor spherical harmonics.