Black holes in the classical and quantum world

Abstract: These are the lecture notes for an introductory course on black holes and some aspects of their interaction with the classical and quantum world. The focus is on phenomena of "fundamental physics" in the immediate surroundings of the black hole (classical and quantum fields, with little astrophysics). We aim more at qualitative, intuitive understanding than at quantitative rigor or detail. Accordingly, we only assume previous exposure to a conventional introduction to the elements of General Relativity and a glancing acquaintance with the Schwarzschild solution, but not more. We use many figures for illustrations and provide a set of carefully guided exercises. Topics: (1) The black hole as a tale of light and darkness. (2) The black hole that vibrates. (3) The black hole that rotates. (4) The black hole that evaporates. (A) Guided problems.