Abstract
It is known that spherically symmetric space–times admit flat space-like foliations. In this paper a simple procedure for the complete foliation of the Schwarzschild space–time by flat space-like hypersurfaces is developed, using the fact that unforced geodesics are orthogonal to such hypersurfaces. The method is then extended to obtain a complete foliation of the Reissner–Nordström space–time by such hypersurfaces. In this case, as there is a barrier beyond which the geodesics do not go, a complete foliation is obtained by analytically continuing the hypersurfaces beyond the barrier. A duality between imaginary time-like geodesics and space-like hypersurfaces is noted, which also provides complete foliation — but the hypersurfaces are not flat. The features of our foliation are discussed.
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