Relativistic Closed-Form Hamiltonian for Many-Body Gravitating Systems in the Post-Minkowskian Approximation

Article

Relativistic Closed-Form Hamiltonian for Many-Body Gravitating Systems in the Post-Minkowskian Approximation

Ledvinka T.; Schäfer G.; Bičák J.

Phys. Rev. Lett. 100, 251101 (2008)

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.

Institute authors

Supported by

GACR 202/06/0041 — Contemporary problems of general relativity and gravitation
LC06014 — Centrum teoretické astrofyziky
MSM0021620860 — Fyzikální studium objektů a procesů ve sluneční soustavě a v astro-fyzikálních systémech

BibTeX

@article{UTF335,
  author        = {Ledvinka T. and Schäfer G. and Bičák J.},
  title         = {{Relativistic Closed-Form Hamiltonian for Many-Body Gravitating Systems in the Post-Minkowskian Approximation}},
  journal       = {Phys. Rev. Lett.},
  volume        = {100},
  pages         = {251101},
  year          = {2008},
  doi           = {10.1103/PhysRevLett.100.251101},
  eprint        = {http://arxiv.org/abs/0807.0214},
  archivePrefix = {arXiv},
}