Gravitational action and gravitational energy

R.F. Polishchuk1


We compare the Hilbert-Einstein gravitational action and the Gibbons-Hawking with a surface term. The equivalence principle is considered as an argument in favor of choosing both the physical vacuum and the action without second-order derivatives of the tetrad potential. This action coincides with Hilbert's under weak Lorentz gauge of the tetrad, i.e., coclosedness of a single 1-form of the tetrad general extension. The Gibbons-Hawking action is exempted from an artificial addition, introduced by its authors and constraining its applicability in the general case. As is the case in electrodynamics, the Lorentz gauge of the potentials provides positive-definiteness of radiation energy.


  1. G. W. Gibbons and S. W. Hawking, Phys. Rev. D 15, 2752 (1977).
  2. S. W. Hawking, General Relativity (Cambridge University Press, 1979).
  3. L. D. Landau and E.M. Lifshitz, Field Theory (Nauka, Moscow, 1973).
  4. J. L. Synge, Relativity: The General Theory (Amsterdam, 1960).
  5. V. A. Fock, Theory of Space, Time and Gravity (Moscow, 1961).
  6. R. F. Polishchuk, Energy-momentum problem in general relativity, GR14 Abstracts, 6-12 August 1995, Florence, Italy, pp. D39, A130.
  7. R. F. Polishchuk, Maxwellization of the Einstein tetrad equations, Astronomical and Astrophysical Transactions 10, 83-84 (1996).
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