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Understood in terms of pure states evolving into mixed states, thepossibility of information loss in black holes is closely related to the globalcausal structure of spacetime, as is the existence of event horizons. However,black holes need not be defined by event horizons, and in fact we argue that inorder to have a fully unitary evolution for black holes, they should be definedin terms of something else, such as a trapping horizon. The Misner-Sharp massin spherical symmetry shows very simply how trapping horizons can give rise toblack hole thermodynamics, Hawking radiation and singularities. We show how theMisner-Sharp mass can also be used to give insights into the process ofcollapse and evaporation of locally defined black holes.

Spherically symmetric trapping horizons, the Misner-Sharp mass and black hole evaporation