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1997 | 41 | 2 | 43-53
Tytuł artykułu

Post-Newtonian approximations and equations of motion of general relativity

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A post-Newtonian approximation scheme for general relativity is defined using the Arnowitt-Deser-Misner formalism. The scheme is applied to perfect fluids and point-mass systems. The two-body point-mass Hamiltonian is given explicitly up to the post$^{2.5}$-Newtonian order.
Słowa kluczowe
Rocznik
Tom
41
Numer
2
Strony
43-53
Opis fizyczny
Daty
wydano
1997
Twórcy
  • Max-Planck-Arbeitsgruppe Gravitationstheorie, Friedrich-Schiller-Universität, 07743 Jena, Germany
Bibliografia
  • [1] V. I. Arnold, Sur la géometrie differentielle des groupes de Lie de dimension infinie et ses applications a l'hydrodynamique des fluids parfaits, Ann. Inst. Fourier (Grenoble) 16 (1966), 319-361.
  • [2] R. Arnowitt, S. Deser, and C. M. Misner, Gravitational-electromagnetic coupling and the classical self-energy problem, Phys. Rev. 120 (1960), 313-320.
  • [3] R. Arnowitt, S. Deser, and C. M. Misner, The dynamics of general relativity, in: Gravitation: An Introduction to Current Research, L. Witten (ed.), Wiley, New York 1962, 227-265.
  • [4] L. Blanchet, Energy losses by gravitational radiation in inspiralling compact binaries to five halves post-Newtonian order, Phys. Rev. D 54 (1996), 1417-1438.
  • [5] L. Blanchet, T. Damour, B. R. Iyer, C. M. Will, and A. G. Wiseman, Gravitational-radiation damping of compact systems to second post-Newtonian order, Phys. Rev. Lett. 74 (1995), 3515-3518.
  • [6] L. Blanchet and G. Schäfer, Higher-order gravitational radiation losses in binary systems, Mon. Not. R. astr. Soc. 239 (1989), 845-867; and Erratum: Mon. Not. R. astr. Soc. 242 (1990), 704.
  • [7] L. Blanchet and G. Schäfer, Gravitational wave tails and binary star systems, Class. Quantum Grav. 10 (1993), 2699-2721.
  • [8] T. Damour, Gravitational radiation and the motion of compact objects, in: Gravitational Radiation, N. Deruelle and T. Piran (eds.), North-Holland Publishing, Amsterdam 1983, 59-144.
  • [9] T. Damour, The problem of motion in Newtonian and Einsteinian gravity, in: 300 Years of Gravitation, S. W. Hawking and W. Israel (eds.), Cambridge University Press, Cambridge 1987, 128-198.
  • [10] T. Damour, L. P. Grishchuk, S. M. Kopejkin, and G. Schäfer, Higher-order relativistic dynamics of binary systems, in: Proc. 5th Marcel Grossmann Meeting on General Relativity, The University of Western Australia 1988, D. G. Blair and M. J. Buckingham (eds.), World Scientific, Singapore 1989, 451-459.
  • [11] T. Damour and G. Schäfer, Lagrangians for n point masses at the second post- Newtonian approximation to general relativity, General Relativity and Gravitation 17 (1985), 879-905.
  • [12] T. Damour and G. Schäfer, Higher-order relativistic periastron advances and binary pulsars, Nuovo Cimento B 101 (1988), 127-176.
  • [13] T. Damour and G. Schäfer, Redefinition of position variables and the reduction of higher order lagrangians, Journ. Math. Phys. 32 (1991), 127-134.
  • [14] B. S. DeWitt, Quantum theory of gravity. I. The canonical theory, Phys. Rev. 160 (1967), 1113-1148.
  • [15] J. Ehlers, Über den Newtonschen Grenzwert der Einsteinschen Gravitationstheorie, in: Grundlagenprobleme der modernen Physik, J. Nitsch, J. Pfarr, and E.-W. Stachow (eds.), Bibliographisches Institut, Mannheim 1981, 65-84.
  • [16] L. P. Grishchuk and S. M. Kopejkin, Equations of motion for isolated bodies with relativistic corrections including the radiation reaction force, in: Relativity in Celestial Mechanics and Astrometry, J. Kovalevsky and V. A. Brumberg (eds.), Reidel, Dordrecht 1986, 19-34.
  • [17] D. D. Holm, Hamiltonian formalism for general-relativistic adiabatic fluids, Physica 17D (1985), 1-36.
  • [18] B. R. Iyer and C. M. Will, Post-Newtonian gravitational radiation reaction for two-body systems: Nonspinning bodies, Phys. Rev. D 52 (1995), 6882-6893.
  • [19] P. Jaranowski and G. Schäfer, Radiative 3.5 post-Newtonian ADM Hamiltonian for many-body point-mass systems, Phys. Rev. D (1996), submitted.
  • [20] W. Junker, G. Schäfer, Binary systems: higher order gravitational radiation damping and wave emission, Mon. Not. R. astr. Soc. 254 (1992), 146-164.
  • [21] S. M. Kopejkin, General-relativistic equations of binary motion for extended bodies, with conservative corrections and radiation damping, Sov. Astron. 29 (1985), 516-524.
  • [22] T. Ohta, H. Okamura, T. Kimura, and K. Hiida, Coordinate condition and higher order gravitational potential in canonical formalism, Progress of Theoretical Physics 51 (1974), 1598-1612.
  • [23] P. C. Peters, Gravitational radiation and the motion of two point masses, Phys. Rev. 136 (1964), B1224-B1232.
  • [24] T. Regge and T. Teitelboim, Role of surface integrals in the Hamiltonian formulation of general relativity, Annals of Physics 88 (1974), 286-318.
  • [25] G. Schäfer, The gravitational quadrupole radiation-reaction force and the canonical formalism of ADM, Ann. Phys. (N.Y.) 161 (1985), 81-100.
  • [26] G. Schäfer, Higher-order post-Newtonian hydrodynamics, in: Proc. 5th Marcel Grossmann Meeting on General Relativity, The University of Western Australia 1988, D. G. Blair and M. J. Buckingham (eds.) World Scientific, Singapore, 1986, 467-470.
  • [27] G. Schäfer, Reduced Hamiltonian formalism for general-relativistic adiabatic fluids and applications, Astron. Nachrichten 311 (1990), 213-217.
  • [28] G. Schäfer, The general relativistic two-body problem. Theory and experiment, in: Symposia Gaussiana, Proc. 2nd Gauss Symposium, Conf. A: Mathematical and Theoretical Physics, Munich 1993, M. Behara, R. Fritsch, and R. G. Lintz (eds.), Walter de Gruyter, Berlin 1995, 667-679.
  • [29] G. Schäfer and N. Wex, Second post-Newtonian motion of compact binaries, Phys. Lett. A 174 (1993), 196-205; and Erratum: Phys. Lett. A 177 (1993), 461.
  • [30] K. Sundermeyer, Constraint Dynamics, Lecture Notes in Physics 169, Springer-Verlag, Berlin 1982.
  • [31] K. S. Thorne, Multipole expansion of gravitational radiation, Rev. Mod. Phys. 52 (1980), 299-339.
  • [32] N. Wex and R. Rieth, The solution of the second post-Newtonian two-body problem, in: Symposia Gaussiana, Proc. 2nd Gauss Symposium, Conf. A: Mathematical and Theoretical Physics, Munich 1993, M. Behara, R. Fritsch, and R. G. Lintz (eds.), Walter de Gruyter, Berlin 1995, 681-693.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
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