  We propose that the space-time evolution of strongly coupled matter formed by
ultra-relativistic heavy ion collisions can be modelled by phenomenological
equations involving the energy-momentum tensor and conserved currents alone.
These equations can describe the late stage of local chemical and thermal
equilibration of the matter formed after collisions, and its subsequent
transition to hydrodynamic expansion in an unified framework. The full set of
equations include local energy, momentum and charge conservation; but also
additional equations for evolution of non-equilibrium variables. These
equations with precisely determined phenomenological parameters can be obtained
by the AdS/CFT correspondence. On the gravity side of this correspondence, for
vanishing chemical potentials, these phenomenological equations give all
solutions of pure gravity in AdS which have regular future horizons. We also
discuss field-theoretic grounds for validity of these phenomenological
equations.
