MG11 |
Participant |
Boccaletti, Dino | |
|
Institution |
Dept. of Mathematics - Piazzale Aldo Moro 5 - Rome - - ITALY | |
|
Session |
Talk |
Abstract |
|
GT6 |
A THEOREM OF BELTRAMI AND THE INTEGRATION OF THE GEODESIC EQUATIONS |
We revisit a not widely known theorem due to Beltrami, through which the integration of the geodetic equations of a curve 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. |