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A theorem of beltrami and the integration of the geodesic equations

TitoloA theorem of beltrami and the integration of the geodesic equations
Tipo di pubblicazionePresentazione a Congresso
Anno di Pubblicazione2008
AutoriBoccaletti, D., Catoni F., Cannata R., and Zampetti P.
Conference Name11th Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Gravitation and Relativistic Field Theories - Proc. of the MG11 Meeting on General Relativity
Conference LocationBerlin
Parole chiaveBeltrami, General solutions, Geodesic equations, geodesy, Gravitation, Hamilton-Jacobi, Integral equations, Relativity, Schwarzschild
Abstract

We revisit a not widely known theorem due to Beltrami, through which the integration of the geodesic equations of a curved manifold is accomplished by a method which is purely geometric although inspired by the Hamilton-Jacobi method. The application of the theorem to Schwarzschild and Kerr metrics leads straight to the general solution of their geodesic equations. As a consequence, we re-obtain the results of Droste and Schwarzschild and of Carter and Walker-Penrose in a simpler way. © 2008 World Scientific Publishing Co. Pte. Ltd.
URLhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-84892989751&partnerID=40&md5=944f1cca30a5741c5853e0a6eef6efe8
Citation KeyBoccaletti20082261