Newton Potential in General Relativity in a Finite Volume

Cover Page

Cite item

Full Text

Abstract

The Newton potential is calculated in the Hamiltonian approach to general relativity (GR) in finite volume, where coordinate ``time'' is gauge-invariant and therefore can't be considered as a measurable variable of the theory. The evolution (gauge-invariant) parameter under study is identified with a homogenous cosmological scale factor $a(x^0)$, determined by means of averaging logarithm of spatial metric determinant over the scale-invariant Licnerowicz space, whereas respective gauge-invariant energy in GR is determined as a solution of the energy constraint equation in relation to the canonical momentum of the scale factor. In this case, cosmological generalization of the Newton potential, given in a non-homogenous class of functions, is specified.

About the authors

I. V. Amirkhanov

Joint Institute for Nuclear Research

6, Joliot-Curie str., Dubna, Moscow Region, 141980, Russia

B. M. Barbashov

Joint Institute for Nuclear Research

6, Joliot-Curie str., Dubna, Moscow Region, 141980, Russia

A. A. Gusev

Joint Institute for Nuclear Research

6, Joliot-Curie str., Dubna, Moscow Region, 141980, Russia

V. N. Pervushin

Joint Institute for Nuclear Research

6, Joliot-Curie str., Dubna, Moscow Region, 141980, Russia

S. A. Shuvalov

Joint Institute for Nuclear Research

6, Joliot-Curie str., Dubna, Moscow Region, 141980, Russia

S. I. Vinitsky

Joint Institute for Nuclear Research

6, Joliot-Curie str., Dubna, Moscow Region, 141980, Russia

A. F. Zakharov

Joint Institute for Nuclear Research

6, Joliot-Curie str., Dubna, Moscow Region, 141980, Russia

V. A. Zinchuk

Joint Institute for Nuclear Research

6, Joliot-Curie str., Dubna, Moscow Region, 141980, Russia

References

  1. Einstein A. Die Gru¨ndlange der allgemeinen Relativit¨atstheorie // Ann. d. Phys. - Vol. 49. - 1916. - Pp. 769-826.
  2. Hilbert D. Die Grundlangen der Physik // Nachrichten von der K¨on. Ges. der Wissenschaften zu G¨ottingen, Math.-Phys. Kl. - Vol. 3. - 1915. - Pp. 395-407.
  3. Noether E. Invariante Variationsprobleme // G¨ottinger Nachrichten, Math.-Phys. Kl. - Vol. 2. - 1918. - Pp. 235-251.
  4. Fock V. A. Geometrisierung der Diracschen Theorie des Electrons // Zs. Phys. - Vol. 57. - 1929. - Pp. 261-277.
  5. Dirac P. A. M. Generalized Hamiltonian Dynamics // Proc. Roy. Soc. - Vol. A 246. - London: 1958. - Pp. 326-332.
  6. Arnowitt R., Deser S., Misner C. W. Canonical Variables for General Relativity // Phys. Rev. - Vol. 117. - 1960. - Pp. 1595-1602.
  7. Zelmanov A. L. Kinemetric Invariants and Their Relation to Chronometric Ones in Einstein’s Gravitation Theory // Dokl. AN USSR. - Vol. 209. - 1973. - Pp. 822-825.
  8. Vladimirov Y. S. Frame of References in Theory of Gravitation. - Moscow: Energoizdat, 1982. - Vol. 209, Pp. 822-825. - In Russian.
  9. Lifshits E. M. On the Gravitational Stability of the Expanding Universe // ZhETF. - Vol. 16. - 1946. - Pp. 587-602.
  10. Mukhanov V. F., Feldman H. A., Brandenberger R. H. Theory of Cosmological Perturbations // Phys. Rep. - Vol. 215. - 1992. - Pp. 203-333.
  11. Barbashov B. M. et al. Hamiltonian Cosmological Perturbation Theory // Phys. Lett. - Vol. B 633. - 2006. - in press.
  12. Zakharov A. F., Zinchuk V. A., Pervushin V. N. Tetrad Formalism and Frames of References in General Relativity // Physics of Particles and Nuclei. - Vol. 37. - 2006. - to be published.
  13. York J. W. Gravitational Degrees of Freedom and the Initial-Value Problem // Phys. Rev. Lett. - Vol. 26. - 1971. - Pp. 1656-1658.
  14. Pawlowski M., Pervushin V. N. Reparametrization-Invariant Path Integral in GR and “Big Bang” of Quantum Universe // Int. J. Mod. Phys. - Vol. A 16. - 2001. - Pp. 1715-1742.
  15. Pervushin V., Smirichinski V. Bogoliubov Quasiparticles in Constrained Systems // J. Phys. A: Math. Gen. - Vol. 32. - 1999. - Pp. 6191-6201.

Supplementary files

Supplementary Files
Action
1. JATS XML
Download

Copyright (c) 2007 Amirkhanov I.V., Barbashov B.M., Gusev A.A., Pervushin V.N., Shuvalov S.A., Vinitsky S.I., Zakharov A.F., Zinchuk V.A.

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.