Quantum black holes: past, present, future. A guided review from the Schwarzschild solution to the algebra of observables

For half a century after Schwarzschild's 1916 solution, a black hole was a purely geometric object; since 1974 it has also been a thermodynamic one, with a temperature and an entropy proportional to the area of its horizon; and since 2015 it has been an object that is observed directly, through gravitational waves and horizon-scale images. This review follows that development in historical order. The past is the classical theory: the Schwarzschild and Kerr solutions, the singularity theorem, the no-hair results and the area theorem. The present begins with Hawking radiation and the Bekenstein–Hawking entropy, continues with the microscopic counting of that entropy in string theory and the holographic dictionary that grew out of it, and includes the observational programme of the LIGO–Virgo–KAGRA detectors and the Event Horizon Telescope as well as laboratory analogues of the Hawking effect. The future is the set of problems that are open today: the mechanism by which information leaves an evaporating black hole, the islands and replica wormholes that reproduce the Page curve, the question whether the gravitational path integral describes one theory or an ensemble, and the von Neumann algebras of observables in which the generalized entropy of a horizon appears as an ordinary entropy. Each step is stated with its key equations and connected to the primary literature, 123 works with their DOIs or arXiv identifiers. Full-text renderings of most of the papers discussed are available on ScholarlyWiki; an appendix gives the complete reading guide.