Innermost circular orbit of binary black holes at the third post-Newtonian approximation

Abstract

The equations of motion of two point masses have recently been derived at the third post-Newtonian (3PN) approximation of general relativity. From that work we determine the location of the innermost circular orbit (ICO), defined by the minimum of the binary's 3PN energy as a function of the orbital frequency for circular orbits. We find that the post-Newtonian series converges well for equal masses. Spin effects appropriate to corotational black-hole binaries are included. We compare the result with a recent numerical calculation of the ICO in the case of two black holes moving on exactly circular orbits (helical symmetry). The agreement is remarkably good, indicating that the 3PN approximation is adequate to accurately locate the ICO of two black holes with comparable masses. This conclusion is reached with the post-Newtonian expansion expressed in the standard Taylor form, without using resummation techniques such as Pad\'e approximants and/or effective-one-body methods.