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 3PN approximation of general relativity. From that work we determine the location of the innermost circular orbit or 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 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 Padé approximants and/or effective-one-body methods.

21 pages, to appear in Phys. Rev. D (spin effects appropriate to corotational black-hole binaries are included; discussion on the validity of the approximation is added)

References in corpus (5)

• Dimensional regularization of the gravitational interaction of point masses
• Third post-Newtonian dynamics of compact binaries: Noetherian conserved quantities and equivalence between the harmonic-coordinate and ADM-Hamiltonian formalisms
• Binary black holes in circular orbits. II. Numerical methods and first results
• Binary black holes in circular orbits. I. A global spacetime approach
• Comparing the inspiral of irrotational and corotational binary neutron stars

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