Non-relativistic gravitation: from Newton to Einstein and back

  title={Non-relativistic gravitation: from Newton to Einstein and back},
  author={Barak Kol and Michael Smolkin},
  journal={Classical and Quantum Gravity},
  • B. Kol, M. Smolkin
  • Published 26 December 2007
  • Physics
  • Classical and Quantum Gravity
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 non-relativistic gravity (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… 

Figures from this paper

Classical effective field theory for weak ultra relativistic scattering
Inspired by the problem of Planckian scattering we describea classical effective field theory for weak ultra relativistic scattering in which field propagation is instantaneous and transverse and the
Classical energy-momentum tensor renormalization via effective field theory methods
We apply the Effective Field Theory approach to General Relativity, introduced by Goldberger and Rothstein, to study point-like and string-like sources in the context of scalar-tensor theories of
EFT approach to general relativity: correction to EIH Lagrangian due to electromagnetic charge
We extend the Non-Relativistic formulation of General Relativity (NRGR) given in Goldberger et al. (Phys Rev D 73:104029, 2006) to incorporate the effects of electromagnetic charge of the
Radiation reaction at 3.5 post-Newtonian order in effective field theory
We derive the radiation reaction forces on a compact binary inspiral through 3.5 order in the post-Newtonian expansion using the effective field theory approach. We utilize a recent formulation of
Gravitational radiative corrections from effective field theory
In this paper we construct an effective field theory (EFT) that describes long wavelength gravitational radiation from compact systems. To leading order, this EFT consists of the multipole expansion,
Effective field theory for gravitational radiation in scalar-tensor gravity
A light scalar degree of freedom, as the one possibly responsible for the accelerated expansion of the Universe, could leave observable traces in the inspiral gravitational wave signal of binary
Radiation reaction and gravitational waves in the effective field theory approach
We compute the contribution to the Lagrangian from the leading order (2.5 post-Newtonian) radiation reaction and the quadrupolar gravitational waves emitted from a binary system using the effective
Testing gravity with the two-body problem.
Gravitational waves provide a new probe into the strong-field regime of gravity. It is thus essential to identify the predictions of General Relativity on the nature of the two-body problem, and to
Fourth-post-Newtonian exact approximation to general relativity
An approximation to general relativity is presented that agrees with the Einstein field equations up to and including the fourth post-Newtonian (PN) order. This approximation is formulated in a fully
Quadratic-in-spin interactions at fifth post-Newtonian order probe new physics
We obtain all quadratic-in-spin interactions in spinning binaries at the third subleading order in post-Newtonian (PN) gravity, and provide their observable binding energies and their gaugeinvariant


Post-Newtonian corrections to the motion of spinning bodies in nonrelativistic general relativity
In this paper we include spin and multipole moment effects in the formalism used to describe the motion of extended objects recently introduced in hep-th/0409156. A suitable description for spinning
Next-to-leading order gravitational spin1-spin2 coupling with Kaluza-Klein reduction
We use the recently proposed Kaluza-Klein (KK) reduction over the time dimension, within an effective field theory (EFT) approach, to calculate the next-to-leading order gravitational spin1-spin2
Post-Newtonian corrections to the motion of spinning bodies in NRGR
In this paper we include spin and multipole moment effects in the formalism used to describe the motion of extended objects recently introduced in hep-th/0409156. A suitable description for spinning
Gravitational field and equations of motion of spinning compact binaries to 2.5 post-Newtonian order
We derive spin-orbit coupling effects on the gravitational field and equations of motion of compact binaries in the 2.5 post-Newtonian approximation to general relativity, one PN order beyond where
Effective field theory of gravity for extended objects
Using effective field theory (EFT) methods we present a Lagrangian formalism which describes the dynamics of nonrelativistic extended objects coupled to gravity. The formalism is relevant to
The Hyperfine Einstein-Infeld-Hoffmann Potential
We use recently developed effective field theory techniques to calculate the third order post-Newtonian correction to the spin-spin potential between two spinning objects. This correction represents
Gravitational radiation in d>4 from effective field theory
Some years ago, a new powerful technique, known as the classical effective field theory, was proposed to describe classical phenomena in gravitational systems. Here we show how this approach can be
Calculation of the first nonlinear contribution to the general-relativistic spin-spin interaction for binary systems.
This correction represents the first contribution to the spin-spin interaction due to the nonlinear nature of general relativity and will play an important role in forthcoming gravity wave experiments.
Hamiltonian of two spinning compact bodies with next-to-leading order gravitational spin-orbit coupling
A Hamiltonian formulation is given for the gravitational dynamics of two spinning compact bodies to next-to-leading order (G/c{sup 4} and G{sup 2}/c{sup 4}) in the spin-orbit interaction. We use a