research

On the accuracy of the post-Newtonian approximation

Abstract

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.Comment: 20 pages, in "2001: a relativistic spacetime odyssey", Proc. of the 25th Johns Hopkins Workshop, I. Ciufolini, D. Dominici and L. Lusanna (eds.), World Scientific, p. 411 (2001

    Similar works

    Available Versions

    Last time updated on 01/04/2019