  We derive a universal formula for the asymptotic growth of the mean value of
three-point coefficient for Warped Conformal Field Theories (WCFTs), and
provide a holographic calculation in BTZ black holes. WCFTs are two dimensional
quantum field theories featuring a chiral Virasoro and U(1) Kac-Moody algebra,
and are conjectured to be holographically dual to quantum gravity on
asymptotically AdS$_3$ spacetime with
Comp$\grave{\mathrm{e}}$re-Song-Strominger boundary conditions. The WCFT
calculation amounts to the calculation of one-point functions on torus, whose
high temperature limit can be approximated by using modular covariance of WCFT,
similar to the derivation of Cardy formula. The bulk process is given by a
tadpole diagram, with a massive spinning particle propagates from the infinity
to the horizon, and splits into particle and antiparticle which annihilate
after going around the horizon of BTZ black holes. The agreement between the
bulk and WCFT calculations indicates that the black hole geometries in
asymptotically AdS$_3$ spacetimes can emerge upon coarse-graining over
microstates in WCFTs, similar to the results of Kraus and Maloney in the
context of AdS/CFT[arXiv:1608.03284].
