# Technicalities in the calculation of the 3rd post-Newtonian dynamics

Banach Center Publications (1997)

- Volume: 41, Issue: 2, page 55-63
- ISSN: 0137-6934

## Access Full Article

top## Abstract

top## How to cite

topJaranowski, Piotr. "Technicalities in the calculation of the 3rd post-Newtonian dynamics." Banach Center Publications 41.2 (1997): 55-63. <http://eudml.org/doc/252187>.

@article{Jaranowski1997,

abstract = {Dynamics of a point-particle system interacting gravitationally according to the general theory of relativity can be analyzed within the canonical formalism of Arnowitt, Deser, and Misner. To describe the property of being a point particle one can employ Dirac delta distribution in the energy-momentum tensor of the system. We report some mathematical difficulties which arise in deriving the 3rd post-Newtonian Hamilton's function for such a system. We also offer ways to overcome partially these difficulties.},

author = {Jaranowski, Piotr},

journal = {Banach Center Publications},

keywords = {ADM formalism; point-particle system; energy-momentum tensor},

language = {eng},

number = {2},

pages = {55-63},

title = {Technicalities in the calculation of the 3rd post-Newtonian dynamics},

url = {http://eudml.org/doc/252187},

volume = {41},

year = {1997},

}

TY - JOUR

AU - Jaranowski, Piotr

TI - Technicalities in the calculation of the 3rd post-Newtonian dynamics

JO - Banach Center Publications

PY - 1997

VL - 41

IS - 2

SP - 55

EP - 63

AB - Dynamics of a point-particle system interacting gravitationally according to the general theory of relativity can be analyzed within the canonical formalism of Arnowitt, Deser, and Misner. To describe the property of being a point particle one can employ Dirac delta distribution in the energy-momentum tensor of the system. We report some mathematical difficulties which arise in deriving the 3rd post-Newtonian Hamilton's function for such a system. We also offer ways to overcome partially these difficulties.

LA - eng

KW - ADM formalism; point-particle system; energy-momentum tensor

UR - http://eudml.org/doc/252187

ER -

## References

top- [1] R. Arnowitt, S. Deser, and C. W. Misner, The dynamics of general relativity, in: Gravitation: an introduction to current research, L. Witten (ed.), Wiley, New York, 1962, 227-265.
- [2] I. M. Gel'fand and G. E. Shilov, Generalized functions, Academic Press, New York, 1964.
- [3] P. Jaranowski and G. Schäfer, Radiative 3.5 post-Newtonian ADM Hamiltonian for many-body point-mass systems, Phys. Rev. D (1996), submitted.
- [4] P. Jaranowski and G. Schäfer, 3rd post-Newtonian ADM Hamiltonian for two-body point-mass systems, in preparation.
- [5] S. M. Kopeikin, General-relativistic equations of binary motion for extended bodies with conservative corrections and radiation damping, Sov. Astron. 29 (1985), 516-524.
- [6] T. Ohta, H. Okamura, T. Kimura, and K. Hiida, Higher order gravitational potential for many-body system, Progr. Theor. Phys. 51 (1974), 1220-1238.
- [7] M. Riesz, L'intégrale de Riemann-Liouville et le problème de Cauchy, Acta Mathematica 81 (1949), 1-223.
- [8] G. Schäfer, The gravitational quadrupole radiation-reaction force and the canonical formalism of ADM, Annals of Physics 161 (1985), 81-100.

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.