Question: How does information get out of the black hole?
Proposed options:
It doesn't get out -- black hole doesn't evaporate fully, information is in remnants.
*Problem*: Pathological properties. Remnants of the Planck scale (where Hawking's black hole radiation calculations fail) enclose a huge amount of entropy.
Information never falls through the horizon ("brick wall").
*Problem*: Violates equivalence principle (if the black hole is huge, horizon isn't a special place since the curvature is small).
Information is copied at the horizon; one copy falls in, one copy stays outside.
*Problem*: Violates no cloning theorem.
Are there corrections to Hawking's calculations at early times (when the black hole is still big)?
*Problem*: Yes, but the horizon is weakly curved, so quantum gravity effects are essentially negligible at early times.
At late times, quantum gravity effects are big, so expect big corrections to Hawking's calculations.
*Problem*: Doesn't work for an interesting reason. ([hep-th/9306083](http://arxiv.org/abs/hep-th/9306083))
*Idea*: By the time black hole is of Planck size, most mixed information is already radiated out. So by the late stages of evaporation, the entanglement between the inside and outside of the black hole is already very small. Non-pureness of the state is mainly contained in the thermal radiation, not in the entanglement entropy.
- ???
---Stanford PHYSICS 134 last lecture (12/04/2013), Autumn 2013-2014, by Sean Hartnoll.