Interpretation of Singularities in General Relativity and the Information Loss Paradox (version 2)

When matter is falling into a black hole, the associated information becomes unavailable to the black hole's exterior. If the black hole disappears by Hawking evaporation, the information seems to be lost in the singularity, leading to Hawking's information paradox: the unitary evolution seems to be broken, because a pure separate quantum state can evolve into a mixed one. This article proposes a new interpretation of the black hole singularities, which restores the information conservation. For the Schwarzschild black hole, it presents new coordinates, which move the singularity at the future infinity (although it can still be reached in finite proper time). For the evaporating black holes, this article shows that we can still cure the apparently destructive effects of the singularity on the information conservation. For this, we propose to allow the metric to be degenerate at some points, and use the singular semiriemannian geometry. This view, which results naturally from Ashtekar's new variables formulation of Einstein's equation, repairs the incomplete geodesics. The reinterpretation of singularities suggested here allows (in the context of standard General Relativity) the information conservation and unitary evolution to be restored, both for eternal and for evaporating black holes.