2007/04/30 by Thomas Mitchell, Thomas P. Mitchell, Clifford M. Will
Physics and Astronomy · #Astrophysical Phenomena and Observations #Cosmology and Gravitation Theories #Pulsars and Gravitational Waves Research #gr-qc
paper · pdf · doi:10.1103/physrevd.75.124025
published as Phys.Rev.D75:124025,2007 · 14 pages, submitted to Phys. Rev. D; small changes to coincide with published version
openalex publication_date 2007/06/29 · arxiv created 2007/07/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Using post-Newtonian equations of motion for fluid bodies valid to the second post-Newtonian order, we derive the equations of motion for binary systems with finite-sized, nonspinning but arbitrarily shaped bodies. In particular we study the contributions of the internal structure of the bodies (such as self-gravity) that would diverge if the size of the bodies were to shrink to zero. Using a set of virial relations accurate to the first post-Newtonian order that reflect the stationarity of each body, and redefining the masses to include 1PN and 2PN self-gravity terms, we demonstrate the complete cancellation of a class of potentially divergent, structure-dependent terms that scale as s^\ensuremath-1 and s^\ensuremath-5/2, where s is the characteristic size of the bodies. This is further evidence of the strong equivalence principle, and supports the use of post-Newtonian approximations to derive equations of motion for strong-field bodies such as neutron stars and black holes. This extends earlier work done by Kopeikin.