Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2005-02-11
General Relativity and Gravitation, 37(12) (2005) 2261
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
12 pages; corrected typos, journal-ref added
Scientific paper
10.1007/s10714-005-0203-z
We revisit a little known theorem due to Beltrami, through which the integration of the geodesic equations of a curved manifold is accomplished by a method which, even if inspired by the Hamilton-Jacobi method, is purely geometric. The application of this theorem to the Schwarzschild and Kerr metrics leads straightforwardly to the general solution of their geodesic equations. This way of dealing with the problem is, in our opinion, very much in keeping with the geometric spirit of general relativity. In fact, thanks to this theorem we can integrate the geodesic equations by a geometrical method and then verify that the classical conservation laws follow from these equations.
Boccaletti Dino
Cannata Roberto
Catoni Francesco
Zampetti Paolo
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