CHOREOGRAPHY AND GRAVITATIONAL WAVES FOR 2-BODY AND 3-BODY GRAVITATING SYSTEMS

In the framework of general relativity, we discuss choreographic solutions for the three-body problem, where a solution is called choreographic if every massive particles move periodically in a single closed orbit. In general relativity, the periastron shift prohibits a binary system from orbiting in a single closed curve. Remarkably, a “figure-eight” solution is shown to be choreographic even at the PN approximation by carefully examining initial conditions. Next, gravitational waves for two- and three-body gravitating systems are discussed as an inverse problem. It is shown that quadrupole waveforms cannot distinguish these sources at particular configurations, especially through extending the definition of the chirp mass to such a three-body system. Finally, we present a conjecture on N particles for classification of sources with multipolar waveforms.