Postulational approach to schwarzschild’s exterior solution with application to a class of interior solutions
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In order to clarify the physical ideas underlying Schwarzschild’s exterior solution, a postulational derivation is given that does not make use of the field equations. Basically this amounts to replacing two field equations by two postulates, one of which is a strong version of the principle of equivalence and the other, Newton’s inverse square law. These postulates are more general than the approach would indicate and there is actually a class of solutions for static systems with spherical symmetry which satisfy them. The energy-stress tensors producing these solutions have the important property that energy density equals radial stress. Two examples of interior solutions that fulfill these postulates are given: a solid sphere and a hollow shell. The basic properties of these solutions are described and compared with those of Schwarzschild’s interior solution. The solid sphere solution is used to complete a previous discussion of the clock paradox. In an Appendix, the field equations for static systems with spherical symmetry are written in a form that indicates the limitations of the postulates.
Si deriva il campo di Schwarzschild per mezzo di postulati diversi con lo scopo di mettere in chiaro alcuni aspetti fisici di questa soluzione. I postulati particolari sono: una versione forte del principio di equivalenza e la legge « quadrato inverso » di Newton. Si danno due soluzioni interne che soddisfano questi postulati: una sfera solida e un guscio cavo. Si discute la proprietà fondamentale di queste soluzioni e si fa una comparazione con la soluzione interna di Schwarzschild. Si dà un’applicazione della soluzione per la sfera al paradosso dell’orologio. Nell’Appendice si scrive l’equazione del campo di gravitazione nella forma che indica le limitazioni dei postulati.
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