New evaporating black hole solutions in two-dimensional quantum gravity: Back-reaction, end-state, information-loss, and thermodynamics.

摘要

Black hole evaporation through Hawking radiation is essential to maintaining the consistency of the second law of thermodynamics in the presence of black holes. However, within the semiclassical approximation without back-reaction, complete evaporation of a black hole that forms from collapsing matter appears to describe a non-unitary evolution from an initial pure state (that of the collapsing matter) to a final mixed state (that of the thermal Hawking radiation). Such evolution maybe inconsistent with the basic tenets of quantum mechanics and one is left wondering if the information that is encoded in the correlations between the outside world and the interior of a black hole is lost as the black hole evaporates away!;We study a modified two-dimensional (2D) dilaton gravity theory that gives insight into the possible fate of information. Our model is exactly solvable in the semiclassical approximation including back-reaction. We find that infalling null matter in an initially static radiationless spacetime forms a black hole if its energy is above a critical value. However, the end-state geometry remaining after evaporation is a non-singular "semi-infinite" throat--a remnant. Although this remnant has a unique geometry in the semiclassical theory, it contains a strong-coupling region that could possibly accommodate the information missing from Hawking radiation, thus leaving room for unitary evolution.;If the energy of infalling matter is subcritical, it 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.;Contrary to some claims in the literature, we prove that the semiclassical approximation remains valid on a 2D black hole horizon when back-reaction is included. It breaks down only in strong-curvature regions close to the black hole singularity.;Finally, we study thermodynamics of the 2D Witten black hole in a "box" in the Hamiltonian formulation. We obtain the unconstrained Hamiltonian, quantize it, and use it to show that the partition function exists for all values of the radius of and the temperature on the box.