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 $P\propto {\omega }^{1-s}exp(-\frac{2\omega }{{\omega }_{crit}})$. Although they have the common feature of an exponential cutoff above a certain frequency ${\omega }_{crit}=\left(\frac{4}{\pi \delta }\right){\omega }_0$, where ω₀ is the frequency of the orbit, the tensor case has a much broader frequency spectrum than scalar or vector radiation.