Vector and tensor radiation from Schwarzschild relativistic circular geodesics

For the case of high multipoles we give an analytic form of the spectrum of gravitational and electromagnetic radiation produced by a particle in a highly relativistic orbit r0=(3+δ)M around a Schwarzschild black hole of mass M. The general dependence of the power spectrum on the frequency in all three spin cases (s=0 for scalar, s=1 for vector, and s=2 for tensor fields) are summarized by power P∝ ω1−sexp(−2ω/ωcrit). Although they have the common feature of an exponential cutoff above a certain frequency ωcrit=(4/πδ)ω0, where ω 0 is the frequency of the orbit, the tensor case has a much broader frequency spectrum than scalar or vector radiation