What does strong subadditivity tell us about black holes?

Understand

It has been argued that small corrections to evolution arising from non-geometric effects can resolve the information paradox.

• We can get such effects, for example, from subleading saddle points in the Euclidean path integral.
• But an inequality derived in 2009 using strong sub-additivity showed that such corrections {\it cannot} solve the problem.
• As a result we sharpen the original Hawking puzzle: we must either have (A) new (nonlocal) physics or (B) construct hair at the horizon.