Smooth Causal Patches for AdS Black Holes

Understand

We review the paradox of low energy excitations about an AdS black hole.

• An appropriately chosen unitary operator in the boundary theory can create a locally strong excitation near the black hole horizon, whose global energy is small as a result of the gravitational redshift.
• The paradox is that this seems to violate a general rule of statistical mechanics, which states that an operator with energy parametrically smaller than $k T$ cannot create a significant excitation in a thermal system.
• When we carefully examine the position dependence of the boundary unitary operator that produces the excitation and the bulk observable necessary to detect the anomalously large effect, we find that they do not both fit in a single causal patch.