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Dimensional regularization of the gravitational interaction of point masses

Thibault Damour·Piotr Jaranowski·Gerhard Schäfer
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Abstract

We show how to use dimensional regularization to determine, within the Arnowitt-Deser-Misner canonical formalism, the reduced Hamiltonian describing the dynamics of two gravitationally interacting point masses. Implementing, at the third post-Newtonian (3PN) accuracy, our procedure we find that dimensional continuation yields a finite, unambiguous (no pole part) 3PN Hamiltonian which uniquely determines the heretofore ambiguous ``static'' parameter: namely, $ω_s=0$. Our work also provides a remarkable check of the perturbative consistency (compatibility with gauge symmetry) of dimensional continuation through a direct calculation of the ``kinetic'' parameter $ω_k$, giving the unique answer compatible with global Poincaré invariance ($ω_k={41/24}$) by summing $\sim50$ different dimensionally continued contributions.

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Thibault Damour, Piotr Jaranowski, Gerhard Schäfer. 2001-05-11. Dimensional regularization of the gravitational interaction of point masses. https://doi.org/10.1016/s0370-2693(01)00642-6

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