Relativistic three-body effects in black hole coalescence

Three-body interactions are expected to be common in globular clusters and in galactic cores hosting supermassive black holes. We consider an equal-mass binary black hole system in the presence of a third black hole. Using numerically generated binary black hole initial data sets, and first and second-order post-Newtonian (1PN and 2PN) techniques, we find that the presence of the third black hole has non-negligible relativistic effects on the location of the binary's innermost stable circular orbit (ISCO), and that these effects arise at 2PN order. For a stellar-mass black hole binary in orbit about a supermassive black hole, the massive black hole has stabilizing effects on the orbiting binary, leading to an increase in merger time and a decrease of the terminal orbital frequency, and an amplification of the gravitational radiation emitted from the binary system by up to 6%.