Post-Minkowskian Closed-Form Hamiltonian for Gravitating N-Body Systems

Conference paper

Post-Minkowskian Closed-Form Hamiltonian for Gravitating N-Body Systems

Ledvinka, T.; Schäfer, G.; Bičák, J.

In: Proceedings of the 12th Marcel Grossmann Meeting on General Relativity, ed. T Damour, R. Jantzen and R Ruffini, World Scientific Publishing, pp. 719 (2012)

doi ↗ link ↗

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 specisl relativistic effects our Hamiltonian extends the results described in classical textbooks of theoretical physics. As an application, the scattering of relativistic objects in considered.

Note

ISBN-13: 978-9814374514

Institute authors

Supported by

GACR 202/09/0772 — Current problems of gravitation, general relativity and relativistic astrophysics
MSM0021620860 — Fyzikální studium objektů a procesů ve sluneční soustavě a v astro-fyzikálních systémech

BibTeX

@inproceedings{UTF482,
  author        = {Ledvinka, T. and Schäfer, G. and Bičák, J.},
  title         = {{Post-Minkowskian Closed-Form Hamiltonian for Gravitating N-Body Systems}},
  booktitle     = {Proceedings of the 12th Marcel Grossmann Meeting on General Relativity},
  editor        = {T Damour, R. Jantzen and R Ruffini},
  publisher     = {World Scientific Publishing},
  pages         = {719},
  year          = {2012},
  doi           = {10.1142/9789814374552\_0039},
  url           = {https://www.worldscientific.com/doi/10.1142/9789814374552\_0039},
  note          = {ISBN-13: 978-9814374514},
}