The Schwarzschild solution is undoubtedly the best known nontrivial exact solution of Einstein's equations. It was found only a few months after Einstein published his field equations. And, not only is it one of the simplest exact vacuum solutions, but it is also the most physically significant. It is widely applied both in astrophysics and in considerations of orbital motions about the Sun or the Earth. Until recently, it was only on the assumption of the applicability of this space-time that general relativity had been demonstrated to be a superior theory to the classical gravitational theory of Newton, in a quantitatively precise manner. It predicts the tiny departures from Newtonian theory that are observed in orbital motions in the solar system, in the deflection of light by the Sun, in the gravitational redshift of light and in time-delay effects. In addition, it provides a model for a theory of strong gravitational fields that is widely applied in astrophysics in the final stages of stellar evolution and the formation of black holes.
For all these reasons, the properties of the Schwarzschild solution are explained even in the most introductory texts on general relativity. Nevertheless, it is still useful to describe this space-time here as some important concepts, such as black hole horizons and analytic extensions, are best introduced in this context. These concepts and some associated techniques, which arise naturally in the Schwarzschild space-time, will be developed further and applied in the more complicated solutions that will be described in following chapters.
In this chapter, we present the familiar interpretation of the Schwarzschild space-time that is based on the assumption of global spherical symmetry.