Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2005-03-10
Phys.Rev. D71 (2005) 124004
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
60 pages, LaTeX 2e, REVTeX 4, 10 PostScript files (1 figure and 9 Young tableaux used in the text)
Scientific paper
10.1103/PhysRevD.71.124004
Dimensional regularization is applied to the computation of the gravitational wave field generated by compact binaries at the third post-Newtonian (3PN) approximation. We generalize the wave generation formalism from isolated post-Newtonian matter systems to d spatial dimensions, and apply it to point masses (without spins), modelled by delta-function singularities. We find that the quadrupole moment of point-particle binaries in harmonic coordinates contains a pole when epsilon = d-3 -> 0 at the 3PN order. It is proved that the pole can be renormalized away by means of the same shifts of the particle world-lines as in our recent derivation of the 3PN equations of motion. The resulting renormalized (finite when epsilon -> 0) quadrupole moment leads to unique values for the ambiguity parameters xi, kappa and zeta, which were introduced in previous computations using Hadamard's regularization. Several checks of these values are presented. These results complete the derivation of the gravitational waves emitted by inspiralling compact binaries up to the 3.5PN level of accuracy which is needed for detection and analysis of the signals in the gravitational-wave antennas LIGO/VIRGO and LISA.
Blanchet Luc
Damour Thibault
Esposito-Farèse Gilles
Iyer Bala R.
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