Vector and tensor radiation from Schwarzschild relativistic circular geodesics

Abstract

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∝ ω^1−sexp(−2ω/ω_crit). Although they have the common feature of an exponential cutoff above a certain frequency ω_crit=(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.