1206.7087 (Stefano Foffa et al.)

The dynamics of the gravitational two-body problem in the post-Newtonian
approximation at quadratic order in the Newton's constant    [PDF]

Stefano Foffa, Riccardo Sturani

We derive the conservative part of the Lagrangian and the energy of a gravitationally bound two-body system at fourth post-Newtonian order, up to terms quadratic in the Newton's constant. We also show that such terms are compatible with Lorentz invariance and we write an ansatz for the center-of mass position. The remaining terms carrying higher powers of the Newton constant are currently under investigation.

View original: http://arxiv.org/abs/1206.7087