Accuracy of the Post-Newtonian Approximation: Optimal Asymptotic Expansion for Quasi-Circular, Extreme-Mass Ratio Inspirals

Details Accuracy of the Post-Newtonian Approximation: Optimal Asymptotic Expansion for Quasi-Circular, Extreme-Mass Ratio Inspirals Accuracy of the Post-Newtonian Approximation: Optimal Asymptotic Expansion for Quasi-Circular, Extreme-Mass Ratio Inspirals

2008-03-13

arxiv.org/abs/0803.1853v2

Phys.Rev.D77:124006,2008; Erratum-ibid.D83:109901,2011

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

17 pages, 14 figures, 5 Tables, 1 Appendix. We added an Erratum to correct some mistakes in tables and figures. The main concl

Scientific paper

10.1103/PhysRevD.77.124006 10.11

We study the accuracy of the post-Newtonian (PN) approximation and its formal region of validity, by investigating its optimal asymptotic expansion for the quasi-circular, adiabatic inspiral of a point particle into a Schwarzschild black hole. By comparing the PN expansion of the energy flux to numerical calculations in the perturbative Teukolsky formalism, we show that (i) the inclusion of higher multipoles is necessary to establish the accuracy of high-order PN terms, and (ii) the region of validity of PN theory is largest at relative O(1/c^6) (3PN order). The latter result suggests that the series diverges beyond 3PN order, at least in the extreme mass-ratio limit, probably due to the appearance of logarithmic terms in the energy flux. The study presented here is a first formal attempt to determine the region of validity of the PN approximation using asymptotic analysis. Therefore, it should serve as a template to perform similar studies on other systems, such as comparable-mass quasi-circular inspirals computed by high-accuracy numerical relativistic simulations.

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