  Black holes and wormholes in the gravitational path integral can be used to
calculate the statistics of heavy operators. An explicit example in higher
dimensions is provided by thin shells of matter. We study these solutions in 3D
gravity, and reproduce the behavior of black holes and wormholes from the dual
CFT using the large-$c$ conformal bootstrap. The CFT operator that creates a
thin shell black hole is a line defect, so we begin by using the bootstrap to
study the statistics of line defects, both at finite $c$ and in the holographic
large-$c$ limit. The crossing equation leads to a universal formula for the
average high-energy matrix elements of the line defect in any compact, unitary
2d CFT with $c>1$. The asymptotics are controlled by a line defect in Liouville
CFT at the same value of the central charge. At large $c$, three distinct
quantities are related: The statistics of line defects in holographic CFTs, the
individual matrix elements of a line defect in Liouville CFT, and the on-shell
action of black holes and wormholes in 3D gravity. The three calculations match
for black holes, and if the statistics of the line defects are assumed to be
approximately Gaussian, then a class of wormholes is also reproduced by the
dual CFT.
