Introduction to Black Holes

Abstract

In these lectures an introduction to black holes in general relativity is presented. First the Schwarzschild black hole and its properties are discussed by studying the geodesics of light and matter. Several coordinate systems are introduced, and the maximal analytic extension of the Schwarzschild solution is obtained, including a white hole, a second universe, and a non-traversable wormhole. Subsequently the properties of the rotating Kerr black hole are discussed. These include, in particular, the ring singularity, the horizons, frame dragging and the ergoregion. As an interesting astrophysical application the photon region and the black hole shadow are addressed.