The black hole information paradox

“The black hole information paradox concerns the intersection of quantum mechanics and general relativity, so its resolution could point the way towards a quantum theory of gravity. The paradox is a contradiction between our understanding of the limits of our physical theories and the consequences of them. With curvature on the scales of that in our solar system, current physical theories have been very successful experimentally; thus, there seems to exist a “solar system limit” in which the laws of physics reduce to those of quantum field theory. However, Hawking’s argument [Haw75], as formalized into a theorem by Mathur [Mat11] (theorem 3 in this report), shows that a natural interpretation of this limit, along with the existence of a “traditional” black hole(such as a Schwarzschild black hole), leads to a violation of the unitarity of quantum mechanics or physically-objectionable “remnants”. Two resolutions to this paradox are presented. The “firewalls” resolution formulated by [AMPS13] considers the observations of an external observer and an infalling observer, and concludes that high-energy quanta near the horizon of the black hole would prevent the paradox (and evade the theorem, as the black hole would no longer be “traditional”). A subsequent argument by Hayden and Harlow examines the computational complexity of the task presented to the infalling observer, and suggests that perhaps quantum field theory does not hold between “computationally-inaccessible” observables, allowing a resolution of the paradox without firewalls [HH13] (thus evading the theorem by interpreting the solar system limit in a different way)."