The Information Paradox

Saeid Moosavioon (University of Tehran)
Tuesday, 94/10/01 (December 22, 2015), 15:00
seminar room 1

Abstract
In 1976, Hawking proposed that fundamental laws of Quantum Mechanics are not valid in the process of black hole (BH) formation and evaporation. The main idea of this proposal is that there is no (or at least very little) information in the radiation from a BH about the characteristics of the mass which has collapsed to form the BH. Put in other words, information is lost during this process; the so-called information Paradox. In fact, Hawking’s proposal established a deep relationship between Gravitation, Thermodynamics and Quantum Mechanics. Prior to Hawking, Bekenstein had discussed that in order to preserve the second law of Thermodynamics the BH must have entropy. Also he showed this entropy should be proportional to the BH’s horizon area. At this stage Gravitation and Thermodynamics nicely come together. But accepting this claim leads us to the trouble of where exactly the BH entropy comes from. We know from Statistical Mechanics that entropy shows the number of available microstates for a system. For a BH with on hair (no extra information rather than mass, electric charge, and angular momentum) the nature of these microstates is not clear. However, there have been some improvements on solving this problem in the context of String Theory.
But a much more dangerous problem arises from Hawking’s semi-classical calculations in which he showed that not only a BH can radiate but also this radiation is completely thermal; this means if we assign a pure state to a star and let it collapse into a BH then this BH can evaporate and starts to radiate its mass until being completely evaporated. Since this radiation is information free and there’s no access to the internal degrees of freedom of the hole, we come up with mixed state at the end of the evaporation. This is in not accepted by Quantum Mechanics because in this context evolutions are described by unitary transformations and therefore it is forbidden to start with a pure state and come up with a mixed state in the end. In other words information must be conserved. This problem can be expected from the causal structure of the BH’s horizon; if we let the BH radiate, then the properties of this radiation must be independent from the interior degrees of freedom because General Relativity forbids any casual connection between the BH interior and exterior.
In this study, at first we ponder further on the underlying foundations and required crucial concepts for entering this problem. Equipped with required tools, we review different approaches to this problem. Then we study paradoxes like firewall, violation of baryon number conservation, ... arising from the Hawking problem. In the end we review various proposed solutions like BH Complementarity, Page theorem, small corrections to Hawking’s calculations, Ads/CFT correspondence view point, ... and discuss the opposing arguments against each of them. There’s no consensus on any of these solutions.