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Dimensional regularization of the third post-Newtonian dynamics of point particles in harmonic coordinates
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Dimensional regularization is used to derive the equations of motion of two point masses in harmonic coordinates. At the third post-Newtonian (3PN) approximation, it is found that the dimensionally regularized equations of motion contain a pole part [proportional to 1/(d-3)] which diverges as the space dimension d tends to 3. It is proven that the pole part can be renormalized away by introducing suitable shifts of the two world-lines representing the point masses, and that the same shifts renormalize away the pole part of the "bulk" metric tensor g_munu(x). The ensuing, finite renormalized equations of motion are then found to belong to the general parametric equations of motion derived by an extended Hadamard regularization method, and to uniquely determine the heretofore unknown 3PN parameter lambda to be: lambda = - 1987/3080. This value is fully consistent with the recent determination of the equivalent 3PN static ambiguity parameter, omega_s = 0, by a dimensional-regularization derivation of the Hamiltonian in Arnowitt-Deser-Misner coordinates. Our work provides a new, powerful check of the consistency of the dimensional regularization method within the context of the classical gravitational interaction of point particles.
Forward citations
Cited by 5 Pith papers
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Gravitational radiation reaction for compact binary systems at the fourth-and-a-half post-Newtonian order in harmonic coordinates
The 4.5PN radiation-reaction acceleration of nonspinning compact binaries is derived in harmonic coordinates, including a dimensional-regularization pole, and is shown to satisfy flux-balance laws and Lorentz invariance.
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Innermost stable circular orbit of arbitrary-mass compact binaries at fourth post-Newtonian order
A fourth post-Newtonian gauge-invariant instability criterion for binary circular orbits is derived, giving the ISCO location for arbitrary mass ratios and matching numerical results to within about 7-15 percent.
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Tidal contributions to the full gravitational waveform to the second-and-a-half post-Newtonian order
Tidal contributions to all gravitational waveform amplitude modes up to l=7 are derived to 2.5PN for quasi-circular non-spinning compact binaries, with flux and phasing provided at the same order.
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Gravitational waves from a binary source in higher dimensional spacetime with compactified extra dimensions
The claimed -1PN correction to the binary equations of motion is an artifact of an invalid expansion and never becomes larger than the Newtonian term, per the paper's own Eq. (97).
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