2010/03/02 by Tomas Ledvinka, Ledvinka, Tomas, Gerhard Schaefer +3
Physics and Astronomy · #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #gr-qc
paper · pdf · doi:10.48550/arxiv.1003.0561
3 pages, to appear in the proceedings of the 12th Marcel Grossmann Meeting, Paris, July 2009
arxiv created 2010/03/02 · arxiv updated 2010/03/05
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.