Non-Relativistic Gravitation: From Newton to Einstein and Back

Abstract

We present an improvement to the Classical Effective Theory approach to the non-relativistic or Post-Newtonian approximation of General Relativity. The "potential metric field" is decomposed through a temporal Kaluza-Klein ansatz into three NRG-fields: a scalar identified with the Newtonian potential, a 3-vector corresponding to the gravito-magnetic vector potential and a 3-tensor. The derivation of the Einstein-Infeld-Hoffmann Lagrangian simplifies such that each term corresponds to a single Feynman diagram providing a clear physical interpretation. Spin interactions are dominated by the exchange of the gravito-magnetic field. Leading correction diagrams corresponding to the 3PN correction to the spin-spin interaction and the 2.5PN correction to the spin-orbit interaction are presented.

10 pages, 3 figures. v2: published version. v3: Added a computation of Einstein-Infeld-Hoffmann in higher dimensions within our improved ClEFT which partially confirms and partially corrects a previous computation. See notes added at end of introduction

References in corpus (5)

• Higher-order spin effects in the dynamics of compact binaries I. Equations of motion
• Hamiltonian of two spinning compact bodies with next-to-leading order gravitational spin-orbit coupling
• The Hyperfine Einstein-Infeld-Hoffmann Potential
• Instabilities of Black Strings and Branes
• Classical Effective Field Theory and Caged Black Holes

Cited by in corpus (50)

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• Spin induced multipole moments for the gravitational wave flux from binary inspirals to third Post-Newtonian order
• Equivalence of ADM Hamiltonian and Effective Field Theory approaches at next-to-next-to-leading order spin1-spin2 coupling of binary inspirals
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• The fifth-order post-Newtonian Hamiltonian dynamics of two-body systems from an effective field theory approach
• The 6th Post-Newtonian Potential Terms at $O(G_N^4)$
• Tropical Feynman integration in the Minkowski regime
• Scalar QED as a toy model for higher-order effects in classical gravitational scattering
• Effective field theory for gravitational radiation in scalar-tensor gravity
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• Worldline effective field theory of inspiralling black hole binaries in presence of dark photon and axionic dark matter
• N${}^3$LO Quadratic-in-Spin Interactions for Generic Compact Binaries
• N${}^3$LO Spin-Orbit Interaction via the EFT of Spinning Gravitating Objects
• Relativistic effective action of dynamical gravitomagnetic tides for slowly rotating neutron stars
• Quadratic-in-spin interactions at fifth post-Newtonian order probe new physics
• Gravitational radiation in d>4 from effective field theory
• Renormalizing Love: tidal effects at the third post-Newtonian order
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• Quantum Hotspots: Mean Fields, Open EFTs, Nonlocality and Decoherence Near Black Holes
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• The SAGEX Review on Scattering Amplitudes, Chapter 4: Multi-loop Feynman Integrals
• Effective two-body approach to the hierarchical three-body problem: quadrupole to 1PN
• Gravitational Multipole Renormalization
• Gravitational radiation-reaction in arbitrary dimension
• The Delocalized Effective Degrees of Freedom of a Black Hole at Low Frequencies
• Radiating Love: adiabatic tidal fluxes and modes up to next-to-next-to-leading post-Newtonian order
• EFT approach to general relativity: correction to EIH Lagrangian due to electromagnetic charge
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• Fourth-post-Newtonian-exact approximation to General Relativity
• Classical Effective Field Theory for Weak Ultra Relativistic Scattering
• Influence Through Mixing: Hotspots as Benchmarks for Basic Black-Hole Behaviour
• Extremal Love: tidal/electromagnetic deformability, logarithmic running and the weak gravity conjecture
• Worldline EFT treatment of quadratic and cubic gravity theories