Quasi-local black hole horizons: recent advances

Abstract While the early literature on black holes focused on event horizons, subsequently it was realized that their teleological nature makes them unsuitable for many physical applications both in classical and quantum gravity. Therefore, over the past two decades, event horizons have been steadily replaced by quasi-local horizons which do not suffer from teleology. In numerical simulations event horizons can be located as an ‘after thought’ only after the entire space-time has been constructed. By contrast, quasi-local horizons naturally emerge in the course of these simulations, providing powerful gauge-invariant tools to extract physics from the numerical outputs. They also lead to interesting results in mathematical GR, providing unforeseen insights. For example, for event horizons we only have a qualitative result that their area cannot decrease, while for quasi-local horizons the increase in the area during a dynamical phase is quantitatively related to local physical processes at the horizon. In binary black hole mergers, there are interesting correlations between observables associated with quasi-local horizons and those defined at future null infinity. Finally, the quantum Hawking process is naturally described as formation and evaporation of a quasi-local horizon. This article focuses on the dynamical aspects of quasi-local horizons in classical general relativity, emphasizing recent results and ongoing research.