General Relativity and Gravitation

, Volume 29, Issue 3, pp 307–343 | Cite as

A Simple Derivation of Canonical Structure and Quasi-local Hamiltonians in General Relativity

  • Jerzy Kijowski

Abstract

A new method of variation of the gravitational Lagrangian is proposed. This method leads in a simple and straightforward way to the canonical description of the gravitational field dynamics in a finite volume V with boundary. No boundary terms are neglected or subtracted ad hoc. Two different forms of gravitational quasi-local energy are derived. Each of them is equal to the field Hamiltonian, corresponding to a specific way of controlling the field boundary data. They play the role of the “internal energy” and the “free energy” respectively. A relation with the boundary formula governing the thermodynamics of black holes is discussed.

VARIATIONAL PRINCIPLE PSEUDORIEMANNIAN GEOMETRY 

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REFERENCES

  1. 1.
    Novello, M., and Arauju, R. A. (1980). Phys. Rev. D22, 260.Google Scholar
  2. 2.
    Berman, M. S. (1991). Gen. Rel. Grav. 23, 465.Google Scholar
  3. 3.
    Barrow, J. D. (1988). Nucl. Phys. B310, 743.Google Scholar
  4. 4.
    Pimentel, L. O. (1987). Astrophys. Space Sci. 116, 387.Google Scholar
  5. 5.
    Wolf, C. (1991). S.-Afr. Tydskr Fis. 14.Google Scholar
  6. 6.
    Beesham, A. (1994). Gen. Rel. Grav. 26,, 159.Google Scholar
  7. 7.
    Maharaj, S. D., and Naido, R. (1993). Astrophys. Space Sci. 208, 261.Google Scholar
  8. 8.
    Sistero, R. F. (1991). Gen. Rel. Grav. 23, 1265.Google Scholar
  9. 9.
    Berman, M. S. (1983). Nuovo Cimento B74, 182.Google Scholar
  10. 10.
    Berman, M. S. (1990). Int. J. Theor. Phys. 29, 571.Google Scholar
  11. 11.
    Abdel Rahman, A.-M. M. (1990). Gen. Rel. Grav. 22, 655.Google Scholar
  12. 12.
    Grø, Ø. (1990). Astrophys. Space Sci. 173, 191.Google Scholar
  13. 13.
    Murphy, G. (1973). Phys. Rev. D8, 4231.Google Scholar
  14. 14.
    Pimentel, L. O. (1985). Astrophys. Space Sci. 116, 395.Google Scholar
  15. 15.
    Berman, M. S., and Som, M. M. (1990). Int. J. Theor. Phys. 29, 1411.Google Scholar
  16. 16.
    Brans, C., and Dicke, R. H. (1961). Phys. Rev. D124, 203.Google Scholar
  17. 17.
    Özer, M., and Taha, M. O. (1987). Nucl. Phys. B287, 776.Google Scholar
  18. 18.
    Pazamata, Z. (1987). Int. J. Theor. Phys. 31, 2115.Google Scholar
  19. 19.
    Kalligas, D., Wesson, P., and Everitt, C. W. (1992). Gen. Rel. Grav. 24, 351.Google Scholar
  20. 20.
    Beesham, A. (1993). Phys. Rev. D48, 3539.Google Scholar
  21. 21.
    Golda, Z., Heller, M., and Szydlowski, M. (1983). Astrophys. Space Sci. 90, 313.Google Scholar
  22. 22.
    Klimek, Z. (1976). Nuovo Cimento B35, 249.Google Scholar
  23. 23.
    Singh, R. K., and Devi, A. R. (1989). Astrophys. Space Sci. 155, 233.Google Scholar
  24. 24.
    Pimentel, L. O. (1994). Int. J. Theor. Phys. 33, 1335.Google Scholar
  25. 25.
    Berman, M. S. (1990). Int. J. Theor. Phys. 29, 571.Google Scholar
  26. 26.
    Berman, M. S., and Som, M. M. (1989). Phys. Lett. A139, 119.Google Scholar
  27. 27.
    Johri, V. B., and Desikan, K. (1994). Gen. Rel. Grav. 26, 1217.Google Scholar
  28. 28.
    Padmanabhan, T., and Chitre, S. M. (1987). Phys. Lett. A120, 433.Google Scholar

Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • Jerzy Kijowski

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