Abstract
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.
- Received 27 January 2008
DOI:https://doi.org/10.1103/PhysRevLett.100.251101
©2008 American Physical Society
Synopsis
Post-Minkowski gravity
Published 28 July 2008
A “simple” closed-form Hamiltonian for a relativistic system of gravitating particles, which depends only on the particles’ momenta and coordinates, is developed.
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