Information loss in black holes and the global hyperbolicity of spacetimes

Abstract

Hawking's semi-classical description of black hole evaporation has been challenged because observers at future infinity have access to less information than those at past infinity, seemingly in conflict with the canons of quantum mechanics according to which the evolution is unitary. In this project, we intend to argue that, far from paradoxical, the loss of information is a natural consequence that the corresponding semiclassical spacetime is not globally hyperbolic. Then, we intend to explore the fact that the backreaction of Hawking radiation on spacetime is not a direct consequence of the theory. Instead, this is introduced a posteriori to guarantee energy conservation. Thus, we will wonder whether we could conceive a different backreaction leading to a globally hyperbolic spacetime, ensuring the preservation of information on successive Cauchy surfaces, and being still in agreement with the predictions of general relativity and quantum field theory far from the Planck scale.