a Theorem of Beltrami and the Integration of the Geodesic Equations

Details a Theorem of Beltrami and the Integration of the Geodesic Equations a Theorem of Beltrami and the Integration of the Geodesic Equations

Sep 2008

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008mgm..conf.2261b&link_type=abstract

"THE ELEVENTH MARCEL GROSSMANN MEETING On Recent Developments in Theoretical and Experimental General Relativity, Gravitation an

Computer Science

Scientific paper

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.

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