Black holes
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Abstract
Chapter 3 used the Schwarzschild metric to obtain predictions for the Solar System. In this chapter, that metric is derived as the unique static, spherically symmetric solution of the vacuum Einstein field equations. For the Solar System, this vacuum solution must be joined to an “interior solution” describing the interior of the Sun. Such solutions are discussed briefly. If, on the other hand, one assumes “vacuum all the way down,” the solution describes a black hole. The chapter analyzes the geometry and physics of the nonrotating black hole: the event horizon, the Kruskal-Szekeres extension, the horizon as a trapped surface and as a Killing horizon. Penrose diagrams are introduced, and a short discussion is given of the four laws of black hole mechanics.