The black hole information paradox is really a combination of two problems: the causality paradox and the entanglement problem. The causality paradox arises because in the semiclassical approximation infalling matter gets causally trapped inside its own horizon; it is therefore unable to send its information back to infinity if we disallow propagation outside the light cone. We show how the causality paradox is resolved in the fuzzball paradigm. One needs to distinguish between two kinds of Rindler spaces: (a) Rindler space obtained by choosing accelerating coordinates in Minkowski space and (b) 'pseudo-Rindler' space, which describes the region near the surface of a fuzzball. These two spaces differ in their vacuum fluctuations. While low energy waves propagate the same way on both spaces, infalling objects with energies E ≫ T suffer an 'entropy enhanced tunneling' in the pseudo-Rindler spacetime (b); this leads to the nucleation of a fuzzball before the infalling object gets trapped inside a horizon.
I. BLACK HOLE PUZZLESConsider a spherical shell of mass M collapsing to form a black hole. In the semiclassical approximation we find that the shell passes through its horizon at r h = 2GM , and ends at a singularity at r = 0. Hawking found that the vacuum around the horizon is unstable, and leads to the creation of particle pairs [1]. One member of the pair (carrying a net negative energy) falls into the hole and reduces its mass, while the other escapes to infinity as 'Hawking radiation'. While overall energy is conserved, there are two fundamental problems with this evaporation process:(A) The causality paradox: After the shell passes through its horizon, light cones in the region between the shell and the horizon 'point inwards' as shown schematically in fig.1. If we assume that we do not have any 'faster than light' propagation in our theory, then the information in the shell is causally trapped inside the horizon. Thus this information cannot escape to infinity as the hole evaporates away. What happens to this information at the endpoint of evaporation? (B) The entanglement problem: The process of Hawking radiation creates entangled pairs at the horizon; thus we find a monotonically increasing entanglement between the radiation near infinity and the remaining hole. Hawking's original computation was done at leading order in the semiclassical approximation, but the small corrections theorem [2] shows that this monotonic increase cannot be overcome by any source of small corrections to the pair creation process. What happens to this large entanglement near the endpoint of evaporation?These two problems together make up the black hole information paradox.One proposal to resolve both of these problems is the idea of 'remnants': the evaporation process stops due to quantum gravity effects when the hole reaches planck (a) (b) FIG. 1. (a) A shell of mass M is collapsing towards its horizon. (b) If the shell passes through its horizon, then the information it carries is trapped inside the horizon due to the structure...