On the accuracy of the post-Newtonian approximation

Details On the accuracy of the post-Newtonian approximation On the accuracy of the post-Newtonian approximation

2002-07-08

arxiv.org/abs/gr-qc/0207037v3

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

20 pages, in "2001: a relativistic spacetime odyssey", Proc. of the 25th Johns Hopkins Workshop, I. Ciufolini, D. Dominici and

Scientific paper

We apply standard post-Newtonian methods in general relativity to locate the innermost circular orbit (ICO) of irrotational and corotational binary black-hole systems. We find that the post-Newtonian series converges well when the two masses are comparable. We argue that the result for the ICO which is predicted by the third post-Newtonian (3PN) approximation is likely to be very close to the ``exact'' solution, within 1% of fractional accuracy or better. The 3PN result is also in remarkable agreement with a numerical calculation of the ICO in the case of two corotating black holes moving on exactly circular orbits. The behaviour of the post-Newtonian series suggests that the gravitational dynamics of two bodies of comparable masses does not resemble that of a test particle on a Schwarzschild background. This leads us to question the validity of some post-Newtonian resummation techniques that are based on the idea that the field generated by two black holes is a deformation of the Schwarzschild space-time.

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