Effective field theory calculation of conservative binary dynamics at third post-Newtonian order

2011/04/30 by Stefano Foffa, S. Foffa, R. Sturani +1 · 7 citations
Mathematics · Physics and Astronomy · #Algorithm #Binary number #Classical mechanics #Computation #Cosmology and Gravitation Theories #Dynamics (music) #Feynman diagram #Field (mathematics) #Gamma-ray bursts and supernovae #Gravitation #Gravitational field #Mathematical physics #Mathematics #Newtonian dynamics #Newtonian fluid #Order (exchange) #Philosophy #Physics #Pulsars and Gravitational Waves Research #Pure mathematics #Third order #gr-qc #hep-th

paper · pdf · doi:10.1103/physrevd.84.044031

published as Phys.Rev.D84:044031,2011 · 24 pages, 6 figures. Typos corrected and references added in v2. Typos corrected in v3

openalex publication_date 2011/08/09 · arxiv created 2011/11/19 · arxiv updated 2015/03/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We reproduce the two-body gravitational conservative dynamics at third post-Newtonian order for spinless sources by using the effective field theory methods for the gravitationally bound two-body system, proposed by Goldberger and Rothstein. This result has been obtained by automatizing the computation of Feynman amplitudes within a Mathematica algorithm, paving the way for higher-order computations not yet performed by traditional methods.

Citations

• Calculation of the First Nonlinear Contribution to the General-Relativistic Spin-Spin Interaction for Binary Systems
• Dimensional regularization of the third post-Newtonian gravitational wave generation from two point masses
• Three-body equations of motion in successive post-Newtonian approximations
• Canonical formulation of gravitating spinning objects at 3.5 post-Newtonian order
• Numerical modeling of black holes as sources of gravitational waves in a nutshell
• Binary black-hole dynamics at the third-and-a-half post-Newtonian order in the ADM formalism
• The Post-Newtonian Approximation for Relativistic Compact Binaries
• Effective one-body approach to general relativistic two-body dynamics
• Determination of the last stable orbit for circular general relativistic binaries at the third post-Newtonian approximation
• Binary black-hole problem at the third post-Newtonian approximation in the orbital motion: Static part

Cited by

• On higher-derivative effects on the gravitational potential and particle bending
• Conservative dynamics of two-body systems at the fourth post-Newtonian approximation of general relativity
• Near and far zones in two-body dynamics: An effective field theory perspective
• Tidal Effects in the Post-Minkowskian Expansion
• The general relativistic two body problem
• Black holes, gravitational waves and fundamental physics: a roadmap
• Gravitational radiation from inspiralling compact objects: Spin-spin effects completed at the next-to-leading post-Newtonian order