  The AdS/CFT correspondence defines a sector with universal strongly coupled
dynamics in the field theory as the dual of pure gravity in AdS described by
Einstein's equation with a negative cosmological constant. We explain here,
from the field-theoretic viewpoint how the dynamics in this sector gets
determined by the expectation value of the energy-momentum tensor \emph{alone}.
We first show that the Boltzmann equation has very special solutions which
could be \textit{functionally} completely determined in terms of the
energy-momentum tensor alone. We call these solutions \textit{conservative
solutions}. We indicate why conservative solutions should also exist when we
refine this kinetic description to go closer to the exact microscopic theory or
even move away from the regime of weak coupling so that no kinetic description
could be employed. We argue that these \textit{conservative solutions} form the
universal sector dual to pure gravity at strong coupling and large $N$. Based
on this observation, we propose a \textit{regularity condition} on the
energy-momentum tensor so that the dual solution in pure gravity has a smooth
future horizon. We also study if irreversibility emerges only at long time
scales of observation, unlike the case of the Boltzmann equation.
