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 ${\mathcal{r}}_0=(3+\delta )M$ around a Schwarzschild black hole of mass $M$. The general dependence of the power spectrum on the frequency in all three spin cases ($s=0\mathrm{}$ for scalar, $s=1\mathrm{}$ for vector, and $s=2\mathrm{}$ for tensor fields) are summarized by power $P\propto {\omega }^{1-s}\exp (-\frac{2\omega }{{\omega }_{\mathrm{crit}}})$. Although they have the common feature of an exponential cutoff above a certain frequency ${\omega }_{\mathrm{crit}}=\left(\frac{4}{\pi \delta }\right){\omega }_0$, where ${\omega }_0$ is the frequency of the orbit, the tensor case has a much broader frequency spectrum than scalar or vector radiation.

• Received 8 June 1972

DOI:https://doi.org/10.1103/PhysRevD.7.1002