Black Hole Horizons and their Mechanics

Abstract: Black holes are often characterized by event horizons, following the literature that laid the mathematical foundations of the subject in the 1970s. However black hole event horizons have two fundamental conceptual limitations. First, they are defined only in space-times that admit a future conformal boundary. Second, they are teleological; their formation and growth is not determined by local physics but depends on what could happen in the distant future. Therefore, event horizons have not played much of a role in the recent theoretical advances that were sparked by discoveries of the LIGO-virgo collaborations. This article focuses on quasi-local horizons that have been used instead. Laws governing them -- mechanics of quasi-local horizons -- generalize those that were first found using event horizons. These results, obtained over the last two decades or so, have provided much insight into dynamical predictions of general relativity in the fully nonlinear regime. The article summarizes the deep and multi-faceted interplay between geometry and physics that has emerged. Conceptually, quasi-local horizons also play a key role in the discussion of the quantum evaporation of black holes. However, due to space limitations, this application is only briefly discussed in Section 6.