Black holes without boundaries

We discuss some of the drawbacks of using event horizons to define black holes and suggest ways in which black holes can be described without event horizons, using trapping horizons. We show that these trapping horizons give rise to thermodynamic behavior and possibly Hawking radiation too. This raises the issue of whether the event horizon or the trapping horizon should be seen as the true boundary of a black hole. This difference is important if we believe that quantum gravity will resolve the central singularity of the black hole and clarifies several of the issues associated with black hole thermodynamics and information loss. 1 What is a black hole? The laws of black hole thermodynamics have been with us for a long time now. They were first derived in the early 1970’s using purely classical general relativity [1]. An important ingredient in the derivation, perhaps the most important ingredient, was the definition of a black hole as the region inside an event horizon. The event horizon, defined mathematically, is the past causal boundary of future null infinity. Even though the concept of a black hole preceded that of an event horizon, because of the work of Hawking and others [2], the event horizon has come to be synonymous with what we mean by a black hole. At the time, there were good reasons for defining a black hole this way. Firstly, event horizons capture the idea of a region from which light, and therefore causal signals, can never escape. The event horizon is a smooth continuous surface and it is easy to locate in stationary spacetimes because it is a Killing horizon. In fact, in static, non-rotating spacetimes the event horizon is just the Killing horizon of the time-translational Killing symmetry. As long as one is