Dimensional regularization of the gravitational interaction of point masses in the ADM formalism
By T. Damour, P. Jaranowski, G. Schāfer. 2001
236 citations recorded by the source corpus.
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, ωs=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 ωk, giving the unique answer compatible with global Poincare invariance (ωk=41/24) by summing ∼50 different dimensionally continued contributions.
Subfields: Astronomy and Astrophysics, Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/f071ea66630ed7ec4396f8555c70933c3a146514
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Citations in the corpus
- The Confrontation between General Relativity and Experiment (2005, methodology): “Itoh and Futamase have used an extension of the Einstein–Infeld–Hoffman matching approach combined with a specific method for taking a point-particle limit [134], while Damour, Jaranowski, and Schäfer have pioneered an ADM Hamiltonian approach that focuses on the equations of motion [139, 140, 77, 7”
- Binary Black Hole Mergers in the First Advanced LIGO Observing Run (2016, background): “[21] LIGO Scientific and Virgo Collaborations, “Erratum: Bi-”
- The Effective Field Theorist's Approach to Gravitational Dynamics (2016, background): “When logarithmic divergences are present, however, we need to dig a little deeper into regularization in d spacetime dimensions (see [193] for another implementation of dim.”
- Black hole binary dynamics from the double copy and effective theory (2019, background): “Later pioneering work derived the full 2PN [13], 3PN [14, 15], and 4PN [16–18] expressions for the conservative potential.”
- Effective one body approach to the dynamics of two spinning black holes with next-to-leading order spin-orbit coupling (2008, background): “1) The orbital Hamiltonian Ho includes the rest-mass contribution and is explicitly known (in ADM-like coordinates) up to the 3PN order [18, 19].”
- GWTC-1: A Gravitational-Wave Transient Catalog of Compact Binary Mergers Observed by LIGO and Virgo during the First and Second Observing Runs (2018, background): “[34] Thibault Damour, Piotr Jaranowski, and Gerhard Schaefer, “Dimensional regularization of the gravitational interaction of point masses,” Phys.”
- Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries (2002, methodology): “[62] argue, clearing up the ambiguity is made possible by the fact that the dimensional regularization, contrary to the Hadamard regularization, respects all the basic properties of the algebraic and differential calculus of ordinary functions.”