ABSTRACT
In this chapter we shall apply the results of Chapters 4 and 6 to some physically relevant space-times of General Relativity, namely Schwarzschild, Reissner-Nordström and Kerr space-times. We shall prove that some open subsets of such space-times have time-convex and light-convex boundary, and the coefficients of the metrics satisfy (3.18) and (3.19), obtaining existence and multiplicity results for timelike and lightlike geodesics. Moreover, in the nondegenerate case, the Morse Relations for light rays are obtained. It is not clear if the boundary of such open sets is convex. For this reason the study of the geodesic connectedeness of such space-times is more difficult (see below). For more physical details on the space-times we shall consider, we refer to [HE, LL].
