Covariant formulation of the post-1-Newtonian approximation to general relativity

@article{Tichy2011CovariantFO,
  title={Covariant formulation of the post-1-Newtonian approximation to general relativity},
  author={Wolfgang Tichy and Eanna E. Flanagan},
  journal={Physical Review D},
  year={2011},
  volume={84},
  pages={044038}
}
We derive a coordinate-independent formulation of the post-1-Newtonian approximation to general relativity. This formulation is a generalization of the Newton-Cartan geometric formulation of Newtonian gravity. It involves several fields and a connection, but no spacetime metric at the fundamental level. We show that the usual coordinate-dependent equations of post-Newtonian gravity are recovered when one specializes to asymptotically flat spacetimes and to appropriate classes of coordinates. 
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References

SHOWING 1-10 OF 23 REFERENCES

The post-Newtonian equations of hydrodynamics in general relativity

The standard Eulerian equations of hydrodynamics are generalized to take into account, consistently with Einstein's field equations, all effects of order 1/c. It is further shown that these…

On the definition of post-newtonian approximations

  • A. Rendall
  • Physics
    Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences
  • 1992
A definition of post-newtonian approximations is presented where the whole formalism is derived from a minimal set of axioms. This establishes a link between the existing precise formulation of the…

CONSERVATION LAWS IN GENERAL RELATIVITY AND IN THE POST-NEWTONIAN APPROXIMATIONS.

It is shown how the exact conservation laws of general relativity, expressed in terms of the symmetric energy-momentum complex of Landau and Lifshitz, can be used to determine the various conserved…

Post-Newtonian extension of the Newton - Cartan theory

The theory obtained as a singular limit of general relativity, if the reciprocal velocity of light is assumed to tend to zero, is known to be not exactly the Newton - Cartan theory, but a slight…

On the Newtonian limit of general relativity

We establish rigorous results about the Newtonian limit of general relativity by applying to it the theory of different time scales for non-linear partial differential equations as developed in [4,…

Newtonian and post-Newtonian approximations are asymptotic to general relativity

It is shown for the first time that the approximations are genuine asymptotic approximation to general relativity, and the results will be applied to radiation reaction in binary star systems, to give a proof of the validity of the ''quadrupole formula'' free from any divergences.

Post-Newtonian Theory and the Two-Body Problem

Reliable predictions of general relativity theory are extracted using approximation methods. Among these, the powerful post-Newtonian approximation provides us with our best insights into the…

General-relativistic celestial mechanics. II. Translational equations of motion.

This work is the first to obtain complete and explicit results, in the form of infinite series, for the laws of motion of arbitrarily composed and shaped bodies.

Post-1-Newtonian equations of motion for systems of arbitrarily structured bodies

We give a surface-integral derivation of post-1-Newtonian translational equations of motion for a system of arbitrarily structured bodies, including the coupling to all the bodies' mass and current…

Does back reaction enforce the averaged null energy condition in semiclassical gravity?

  • FlanaganWald
  • Physics
    Physical review. D, Particles and fields
  • 1996
It is suggested that if traversable wormholes do exist as solutions to the semiclassical equations, they cannot be macroscopic but must be ``Planck scale'', in agreement with conclusions drawn by Ford and Roman from entirely independent arguments.