Point-particle limit and the far-zone quadrupole formula in general relativity

T. Futamase

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)


Strong internal gravity is incorporated in a divergent-free post-Newtonian approximation scheme by introducing a body-zone limit. When incorporated into the notion of sequences of solutions, this provides the first rigorous point-particle limit in general relativity. The scheme is applied to construct an asymptotic approximation to a binary system composed of two rotating neutron stars. The lowest-order calculation is carried out in the near and far zones, giving Newtons equations of motion and the far-zone quadrupole formula. The quadrupole moment of the system is expressed in terms of a mass integral over each compact star. The same mass appears in Newtons equations of motion. The mass is indeed the Arnowitt-Deser-Misner mass the compact star would have if it were isolated. Thus the equivalence principle for strong gravity is confirmed, even for gravitational radiation: gravitational potential energy radiates the same amount of gravitational waves as any other form of energy does.

Original languageEnglish
Pages (from-to)2566-2574
Number of pages9
JournalPhysical Review D
Issue number10
Publication statusPublished - 1985

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)


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