A deflexão da luz e o Teorema de Gauss-Bonnet

Abstract

This work aims to present a methodology for the calculation of the angle of light deflection caused by agravitational field. This methodology consists in using the generalized Fermat principle for a space-time with spherical and static symmetry and the Gauss-Bonnet theorem, associating the optical metric with the metric induced in a surface. We present the equations of the gravitational field, some solutions of the field equations and the generalization of the Fermat principle. Some essential definitions of differential geometry a represented and the Gauss-Bonnet theorem is developed. In this work it was possible to understand the focus of the light rays has a topological character, as shown by Gibbons and it was possible to present the methodology that allows to calculate the angle of light deflection that can be used for asymptotically flat spacetime and for non-asymptotically flat spacetime.