  We interpret appropriate families of Euclidean wormhole solutions of AdS$_3$
gravity in individual 2d CFTs as replica wormholes described by branching
around the time-symmetric apparent horizons of black holes sourced by the
backreaction of heavy point particles. These wormholes help describe a rich
formalism to coarse grain pure states in 2d CFTs dual to the black hole
geometries because the wormhole amplitudes match with the Renyi entropies of
CFT states obtained by decohering the pure states in a specific way. This
formalism can be generalised to coarse grain pure states in several copies of
the dual CFT dual to multi-boundary black holes using wormhole solutions with
higher genus boundaries using which we illustrate that coarse graining away the
interior of multi-boundary black holes sets the mutual information between any
two copies of the dual CFT to zero. Furthermore, this formalism of coarse
graining pure states can be extended to decohere transition matrices between
pure states which helps interpret more general families of wormhole solutions
including those with non replica-symmetric boundary conditions in individual
CFTs. The pseudo entropy of the decohered transition matrices has interesting
holographic interpretation in terms of the area of minimal surfaces on
appropriate black hole or wormhole geometries. The wormhole solutions which
show up in the coarse graining formalism also compute the Renyi entropies of
Hawking radiation after the Page time in a setup which generalizes the West
Coast model to 3d gravity. Using this setup, we discuss the evaporation of
one-sided black holes sourced by massive point particles and multi-boundary
black holes in 3d gravity.
