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Title:
Accuracy of the post-Newtonian approximation: Optimal asymptotic expansion for quasicircular, extreme-mass ratio inspirals
Authors:
Yunes, Nicolás; Berti, Emanuele
Affiliation:
AA(Institute for Gravitational Physics and Geometry and Center for Gravitational Wave Physics, Physics Department, The Pennsylvania State University, University Park, Pennsylvania 16802, USA), AB(Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 91109, USA)
Publication:
Physical Review D, vol. 77, Issue 12, id. 124006 (PhRvD Homepage)
Publication Date:
06/2008
Origin:
APS
PACS Keywords:
Post-Newtonian approximation; perturbation theory; related approximations, Numerical studies of black holes and black-hole binaries, Wave generation and sources, Relativity and gravitation
DOI:
10.1103/PhysRevD.77.124006
Bibliographic Code:
2008PhRvD..77l4006Y

Abstract

We study the accuracy of the post-Newtonian (PN) approximation and its formal region of validity, by investigating its optimal asymptotic expansion for the quasicircular, 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/c6) (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 quasicircular inspirals computed by high-accuracy numerical relativistic simulations.
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