A pedagogical approach to the black hole information problem

Abstract: The semiclassical depiction of gravity has provided many important results, such as particle creation effects in expanding universes and in spacetimes containing black holes. However, many questions remain open, most notably concerning the final product of the black hole evaporation process and the conservation of information. From a pedagogical perspective, we review the concepts that lead to this state of affairs, also known as the black hole information problem, and discuss the assumptions and hypotheses necessary for its formulation. Stating the necessary conjectures and results that lead to the geometrical properties of black holes, we present the notion of black hole evaporation and the result that entanglement between causally complementary regions is an intrinsic feature of quantum field theory under the Hadamard condition. We then show that the formation and complete evaporation of a black hole leads to information loss. Comparing such a result to the main alternatives to this non-unitary dynamical evolution, we formulate the black hole information problem and show that information loss is a genuine prediction if no deviations from the semiclassical picture occur at the Planck scale.