### Abstract

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 language | English |
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Pages (from-to) | 2566-2574 |

Number of pages | 9 |

Journal | Physical Review D |

Volume | 32 |

Issue number | 10 |

DOIs | |

Publication status | Published - 1985 |

### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)

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## Cite this

*Physical Review D*,

*32*(10), 2566-2574. https://doi.org/10.1103/PhysRevD.32.2566