Contrasting the fuzzball and wormhole paradigms for black holes

Understand

We examine an interesting set of recent proposals describing a `wormhole paradigm' for black holes.

• These proposals require that in some effective variables, semiclassical low-energy dynamics emerges at the horizon.
• We prove the `effective small corrections theorem' to show that such an effective horizon behavior is not compatible with the requirement that the black hole radiate like a piece of coal as seen from outside.
• This theorem thus concretizes the fact that the proposals within the wormhole paradigm require some nonlocality linking the hole and its distant radiation.