The black hole information paradox has been tightened to a precise contradiction by the small corrections theorem. Resolving the puzzle thus needs an order unity correction to semiclassical dynamics at the horizon. Remarkably, in string theory we find that microstates of black holes are `fuzzballs' with no horizon, which resolves the paradox. An alternative to the fuzzball paradigm is has been sought through a `wormhole paradigm' where the horizon would be continue to be described by semiclassical physics on a code subspace of the full quantum degrees of freedom. This wormhole paradigm can however can be ruled out by an extension of the small corrections theorem. We argue that the notions of ER=EPR etc underlying the wormhole paradigm are incorrect, and that the error arises from using the eternal spacetime geometry which is itself inconsistent with the requirements of unitarity.

The Bekenstein-Hawking formula for the entropy of a black hole suggests that entropy in strong gravity situations should be proportional to bounding area rather than enclosed volume. But we argue that the S and T dualities of string theory suggest an entropy formula that is extensive in the volume, with the area formula appearing as a special case. In particular we find a set of states in string theory that violate the covariant entropy bound, which seeks to extend the area entropy formula to situations like the early Universe.