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L’autore enuncia e risolve il problema di Cauchy per le equazioni di Einstein della relatività unitaria, che vengono convenientemente trasformate dopo essere state dedotte da un principio variazionale.
Risulta allora che le equazioni di campo ammettono un’unica soluzione locale analitica e reale, nell’intorno di una generica ipersuperficie dello spaziotempo sulla quale si assegni il tensore fondamentale e le derivate normali delle due componenti.
L’affermazione precedente cade in corrispondenza ad ipersuperficie la cui equazione è analoga a quella che determina le varietà caratteristiche delle equazioni gravitazionali.
Questa circostanza porta l’Autore a ravvisare in esse i fronti d’onda del campo unitario einsteiniano.
Summary
The author describes and resolves Cauchy’s problem for Einstein’s equations about unitary relativistic theory.
These equations, deduced from a variational principle, are properly transformed.
He proves that field’s equations have one and only one solutiont hat is real and analytical on every generical space-time hypersurface’s neighbourhood, if on this surface the foundamental tensor with normal derivatives of its components are given.
The result is not true only for special hypersurfaces having an equation very similar tho that of characteristic varieties in gravitational theory.
This circustance enambles the author to recognise the wave fronts of unitary Einstein-field.
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Lichnerowicz, A. Etude des équations du champ de la théorie unitaire d’Einstein. Seminario Mat. e. Fis. di Milano 25, 121–133 (1955). https://doi.org/10.1007/BF02923814
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DOI: https://doi.org/10.1007/BF02923814