Signature of chaos in gravitational waves from a spinning particle

A spinning test particle around a Schwarzschild black hole shows chaotic behavior if its spin is larger than a critical value. We discuss whether or not some peculiar signature of chaos appears in the gravitational waves emitted from such a system. Calculating the emitted gravitational waves by use of the quadrupole formula, we find that the energy emission rate of gravitational waves for a chaotic orbit is about 10 times larger than that for a circular orbit, but the same enhancement is also obtained by a regular “elliptic” orbit. A chaotic motion does not always enhance the energy emission rate maximally. As for the energy spectra of the gravitational waves, we find some characteristic feature for a chaotic orbit. It may tell us how to find the chaotic behavior of the system. Such peculiar behavior, if it is found, may also provide some additional information to determine the parameters of a system such as a spin.