Abstract
Spherically symmetric space-times have been studied in general relativity ever since the beginning when as the first exact solution of the Einstein equation the Schwarzschild space-time was given. Later on an elaborate local theory of spherically symmetric space-times was worked out with such fundamental results as Birkhoff ’s theorem and essential results concerning their global geometry have been achieved. Yet it seems that a general global theory is lacking even now. Some fundamental facts concerning the global geometry of spherically symmetric space-times are presented below. The concept of axis and of transverse submanifold are introduced and applied to study and classification. 1. Basic properties of spherically symmetric space-times and the concept of axis Definition. Let (M, 〈, 〉) be a space-time, i.e. a 4-dimensional connected time oriented Lorentz manifold; an isometric action
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