We discuss the relations between the notion of convexity in a Riemannian framework and finiteness of the number of geodesics between two fixed points. The results obtained can be applied to the study of lightlike geodesics joining a point and a timelike curve in a conformally static Lorentzian manifold. These geodesics are interpreted as light rays between a light source and an event of a relativistic spacetime; thus our results may be used for a mathematical description of the gravitational lensing effect.
Convexity and the finiteness of the number of geodesics. Applications to the multiple-image effect / Giannoni, F.; Masiello, A.; Piccione, P.. - In: CLASSICAL AND QUANTUM GRAVITY. - ISSN 0264-9381. - STAMPA. - 16:3(1999), pp. 731-748. [10.1088/0264-9381/16/3/008]
Convexity and the finiteness of the number of geodesics. Applications to the multiple-image effect
Masiello, A.;
1999-01-01
Abstract
We discuss the relations between the notion of convexity in a Riemannian framework and finiteness of the number of geodesics between two fixed points. The results obtained can be applied to the study of lightlike geodesics joining a point and a timelike curve in a conformally static Lorentzian manifold. These geodesics are interpreted as light rays between a light source and an event of a relativistic spacetime; thus our results may be used for a mathematical description of the gravitational lensing effect.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
