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Il Nuovo Cimento (1955-1965)

, Volume 20, Issue 1, pp 1–19 | Cite as

On the energy-momentum tensor of the gravitional field

  • P. E. Tangherlini
Article

Summary

In a previous note it was suggested that x-1Λgμν, with Λ>0 fulfills the basic requirements of a generally covariant energy-momentum tensor for the gravitational field. Some further justification is given for this hypothesis bya) studying the character of the field equations in the absence of the cosmological term;b) a re-interpretation of the line element based on Mach’s principle;c) calculating the gravitational proper energy for de Sitter static universe with and without a Schwarzschild field present and showing that the difference is proportional to the Schwarzschild mass. Finally an attempt is made to define a true tensor for the angular momentum density. It is shown that in this way one is led to a definition of « physical co-ordinates ». These co-ordinates are determined in such a way that in the weak-field limit they approach the usual Lorentz co-ordinates. However it is not possible to arrive at these co-ordinates by imposing co-ordinate conditions, since they form the components of a vector. To the extent that the angular momentum of the gravitational field is covariantly conserved, the co-ordinates may be obtained as the gradient of a world scalar which satisfies an inhomogeneous d’Alembertian equation.

Riassunnto

Si esamina l’ipotesi che il termine cosmologico di Einstein (con Λ> 0) debba easere interpretato come il tensore cnergia-impulso del campo di gravitazione. Una nuova interpretazione dell’elemento lineare è data dal punto di vista di Mach che conduce in maniera naturale alla necessità di questo termine nelle equazioni del campo. Si considera anche il problema di definire un tensore dell’impulso angolare per il campo di gravitazione.

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References

  1. (1).
    F. R. Tangheelini:Nuovo Cimenta,15, 385 (1960).Google Scholar
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    For a recent review of conservation laws seeJ. G. Fletcher:Rev. Mod. Phys.,32, 65 (1960), where further references are given. See also it. Magnusson:Mat. Fys Medd.,32, 6 (1960).MathSciNetADSCrossRefMATHGoogle Scholar
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    V. Fock:The Theory of Space Time and Gravitation (London, 1959).Google Scholar

Copyright information

© Società Italiana di Fisica 1961

Authors and Affiliations

  • P. E. Tangherlini
    • 1
  1. 1.Souola di Perfezionamento in Fisica Teorica e NucleareNapoli

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