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.
@article{bwmeta1.element.bwnjournal-article-bcpv41z2p55bwm,
author = {Jaranowski, Piotr},
title = {Technicalities in the calculation of the 3rd post-Newtonian dynamics},
journal = {Banach Center Publications},
volume = {38},
year = {1997},
pages = {55-63},
zbl = {0891.53063},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv41z2p55bwm}
}
Jaranowski, Piotr. Technicalities in the calculation of the 3rd post-Newtonian dynamics. Banach Center Publications, Tome 38 (1997) pp. 55-63. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv41z2p55bwm/
[000] [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.
[001] [2] I. M. Gel'fand and G. E. Shilov, Generalized functions, Academic Press, New York, 1964.
[002] [3] P. Jaranowski and G. Schäfer, Radiative 3.5 post-Newtonian ADM Hamiltonian for many-body point-mass systems, Phys. Rev. D (1996), submitted.
[003] [4] P. Jaranowski and G. Schäfer, 3rd post-Newtonian ADM Hamiltonian for two-body point-mass systems, in preparation.
[004] [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.
[005] [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.
[006] [7] M. Riesz, L'intégrale de Riemann-Liouville et le problème de Cauchy, Acta Mathematica 81 (1949), 1-223.
[007] [8] G. Schäfer, The gravitational quadrupole radiation-reaction force and the canonical formalism of ADM, Annals of Physics 161 (1985), 81-100.