ABSTRACT
This chapter presents a variety of examples of space-times. In particular, Minkowski space-time, Schwarzschild space-times, Kerr space-times, and Robertson-Walker space-times all have significant physical interpretations. Minkowski space-time is simultaneously the geometry of special relativity and the geometry induced on each fixed tangent space of an arbitrary Lorentzian manifold. Thus Minkowskian geometry plays the same role for Lorentzian manifolds that Euclidean geometry plays for Riemannian manifolds. The Schwarzschild space-times represent the spherically symmetric, empty space-times outside nonrotating, spherically symmetric bodies. These space-times may also be used to model the gravitational fields outside of dead black holes. The gravitational fields outside of rotating black holes apparently correspond to the Kerr space-times. The usual “big bang” cosmological models are based on the Robertson-Walker space-times. These space-times are foliated by a special set of spacelike hypersurfaces such that each hypersurface corresponds to an instant of time.
