Hawking radiation and unitary evolution.

We find a family of exact solutions to the semi-classical equations (including back-reaction) 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 transfers information faster than the theoretical bound for positive energy. Electronic address: [email protected] Electronic address: [email protected] Electronic address: [email protected] 1 Recently we presented a modified two-dimensional (2D) dilaton gravity theory that is exactly solvable semiclassically [1]. In this 2D theory (as in 4D Einstein gravity), infalling null matter forms a black hole only if its energy M is above a certain critical value Mcr. In Ref. [1] we studied the supercritical case, M > Mcr, in which a black hole is formed and evaporates by emitting Hawking radiation. In this work we study the subcritical case, M < Mcr, in which the infalling matter becomes outgoing and escapes to infinity without forming a black hole. Because we can obtain the numerical solution to the future of the classical outgoing matter, we can see how correlations among outgoing created particles preserve unitarity and how Hawking radiation originates as the energy of the infalling matter approaches Mcr. The effective action of the modified 2D dilaton gravity theory is [1]