Hawking radiation and unitary evolution

We find a family of exact solutions to the semiclassical equations (including backreaction) of two-dimensional dilaton gravity, describing infalling null matter that becomes outgoing and returns to infinity without forming a black hole. When a black hole almost forms, the radiation reaching infinity in advance of the original outgoing null matter has the properties of Hawking radiation. The radiation reaching infinity after the null matter consists of a brief burst of negative energy that preserves unitarity and restores correlations rapidly as a result of strong backreaction.