Post-Minkowskian closed-form Hamiltonian for gravitating N-body systems

Details Post-Minkowskian closed-form Hamiltonian for gravitating N-body systems Post-Minkowskian closed-form Hamiltonian for gravitating N-body systems

2010-03-02

arxiv.org/abs/1003.0561v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

3 pages, to appear in the proceedings of the 12th Marcel Grossmann Meeting, Paris, July 2009

Scientific paper

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.

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