  One of the outstanding problems in the holographic approach to many-body
physics is the explicit computation of correlation functions in nonequilibrium
states. We provide a new and simple proof that the horizon cap prescription of
Crossley-Glorioso-Liu for implementing the thermal Schwinger-Keldysh contour in
the bulk is consistent with the Kubo-Martin-Schwinger periodicity and the
ingoing boundary condition for the retarded propagator at any arbitrary
frequency and momentum. The generalization to the hydrodynamic Bjorken flow is
achieved by a Weyl rescaling in which the dual black hole's event horizon
attains a constant surface gravity and area at late time although the
directions longitudinal and transverse to the flow expands and contract
respectively. The dual state's temperature and entropy density thus become
constants (instead of the perfect fluid expansion) although no time-translation
symmetry emerges at late time. Undoing the Weyl rescaling, the correlation
functions can be computed systematically in a large proper time expansion in
inverse powers of the average of the two reparametrized proper time arguments.
The horizon cap has to be pinned to the nonequilibrium event horizon so that
regularity and consistency conditions are satisfied. Consequently, in the limit
of perfect fluid expansion, the Schwinger-Keldysh correlation functions with
space-time reparametrized arguments are simply thermal at an appropriate
temperature. A generalized bilocal thermal structure holds to all orders. We
argue that the Stokes data (which are functions rather than constants) for the
hydrodynamic correlation functions can decode the quantum fluctuations behind
the horizon cap pinned to the evolving event horizon, and thus the initial
data.
