  Many hybrid models of heavy ion collisions construct the initial state for
hydrodynamics from transport models. Hydrodynamics requires that the
energy-momentum tensor $T^{\mu\nu}$ and four-currents $j^{\mu}$ do not deviate
considerably from the equilibrium ideal-fluid form, but the ones constructed
from transport do not necessarily possess this property. In this work we
investigate the space-time picture of $T^{\mu\nu}$ deviations from equilibrium
in Au+Au collisions using a coarse-grained transport approach. The collision
energy is varied in the range $E_{lab} = 5-160A$ GeV. The sensitivity of
$T^{\mu\nu}$ deviations from equilibrium to collision centrality, and other
parameters such as the switching criterion, the amount of statistics used to
construct the initial state, and the smearing parameter $\sigma$ is
investigated. For low statistics deviations of $T^{\mu\nu}$ from equilibrium
are large and dominated by the effect of finite sampling. For large statistics
the pressure anisotropy plays the most significant role, while the off-diagonal
components of $T^{\mu\nu}$ are small in a large volume during the whole
evolution. For all considered energies and centralities the pressure anisotropy
exhibits a similar feature: there is a narrow interval of time, when it rapidly
drops in a considerable volume. This allows us to introduce an "isotropization
time," which is found to decrease with energy and slightly increase with
centrality. The isotropization times are larger than times typically used for
initializing hydrodynamics.
