Relativistic Closed-Form Hamiltonian for Many-Body Gravitating Systems   in the Post-Minkowskian Approximation
  The Hamiltonian for a system of relativistic bodies interacting by their gravitational field is found in the post-Minkowskian approximation, including all terms linear in the gravitational constant. It is given in a surprisingly simple closed form as a function of canonical variables describing the bodies only. The field is eliminated by solving inhomogeneous wave equations, applying transverse-traceless projections, and using the Routh functional. By including all special relativistic effects our Hamiltonian extends the results described in classical textbooks of theoretical physics. As an application, the scattering of relativistic objects is considered. 
Tomas Ledvinka, Gerhard Schaefer and Jiri Bicak