Summary
In this paper we show that the equations of the motion of a free test particle in General Relativity, with respect to any physical system of reference, can always have the classical interpretation:Time derivative of momentum =mass ×gravitational field. The result is reached by means of suitable definitions of the different dynamical quantities relative to the chosen system of reference and by means of the systematic use of a differential operation that generalizes the usual absolute differentiation. In the gravitational field there are present three parts: one deriving from a scalar potential, one similar to Coriolis’ apparent field, and one part deriving from a vector potential.
Riassunto
In questo lavoro si mostra come alle equazioni del moto di una particella libera di prova in Relatività generale, riferite a un generico sistema fisico di riferimento, possa sempre darsi l’interpretazione classica:Derivata temporale dell’impulso =massa ×campo gravitazionale. Lo scopo si raggiunge definendo opportunamente le varie grandezze dinamiche relative al riferimento prescelto, e mediante l’uso sistematico di una operazione differenziale che generalizza l’ordinaria differenziazione assoluta. Nel campo gravitazionale risultano presenti tre parti: una derivante da un potenziale scalare, una analoga al campo apparente del Coriolis, e una parte proveniente da un potenziale vettore.
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References
Cfr.A. Lichnerowicz:Théories relativistes de la gravitation et de l’électromagnétisme (Paris, 1955), p. 8.
See, for example,C. Møller:The Theory of Relativity (Oxford, 1952), p. 248 foll.
J. v. Weyssenhoff:Bull. Acad. Polon., Sec. A, 252 (1937).
Regarding this Sect. 2.1, seeMøller:op. cit., p. 288 segg.
Cfr.Møller:op. cit., p. 291.
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Cattaneo, C. General relativity: Relative standard mass, momentum, energy and gravitational field in a general system of reference. Nuovo Cim 10, 318–337 (1958). https://doi.org/10.1007/BF02732487
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DOI: https://doi.org/10.1007/BF02732487