Abstract
Abstract Chapter 15 introduces the notions of stationary space-time and static space-time. In simple terms, a solution is stationary if it is time independent. On the other hand, the stronger requirement that a solution is static means that it cannot be evolutionary. In such a case, nothing would change if time ran backwards. The definitions for static and stationary space-time are given in terms of both coordinates and, geometrically, hypersurface orthogonal vector fields and Killing vectors. The next section solves the vacuum field equations in spherical symmetry. This then leads to the Schwarzschild exterior solution, which describes the gravitational field outside a spherically symmetric star. The uniqueness of this solution allows one to deduce Birkhoff’s theorem, which states that a spherically symmetric vacuum exterior solution to a star is necessarily static. Finally, the Schwarzschild interior solution is discussed.
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