Future Boundaries and the Black Hole Information Paradox

The black hole information paradox is the incompatibility of quantum mechanics with the semi-classical picture of Hawking radiation. Hawking radiation appears thermal and eventually leads to the complete disappearance of a black hole. However, black holes could be formed from a pure quantum state. The transition from such an initial state to the final state of pure Hawking radiation cannot be described by unitary time evolution. In this paper, we present an analysis in quantum gravity that shows how boundary conditions in the future prevent a loss of quantum mechanical information from the spacetime. In classical physics, the future boundary of the spacetime in the black hole interior is a singularity. Realistic gravitational collapse results in a BKL type of approach to the singularity. But, solving the Wheeler-DeWitt equation reveals that the singularity does not form and can be replaced by specifying a final state density matrix. Such a condition is natural within the context of consistent histories version of quantum mechanics. We provide a self-contained treatment of these issues. How information escapes from the black hole will be treated elsewhere.