  Nuclei colliding at very high energy create a strong, quasi-classical gluon
field during the initial phase of their interaction. We present an analytic
calculation of the initial space-time evolution of this field in the limit of
very high energies using a formal recursive solution of the Yang-Mills
equations. We provide analytic expressions for the initial chromo-electric and
chromo-magnetic fields and for their energy-momentum tensor. In particular, we
discuss event-averaged results for energy density and energy flow as well as
for longitudinal and transverse pressure of this system. For example, we find
that the ratio of longitudinal to transverse pressure very early in the system
behaves as $p_L/p_T =
-[1-\frac{3}{2a}(Q\tau)^2]/[1-\frac{1}{a}(Q\tau)^2]+\mathcal{O}(Q\tau)^4$ where
$\tau$ is the longitudinal proper time, $Q$ is related to the saturation scales
$Q_s$ of the two nuclei, and $a = \ln (Q^2/\hat{m}^2)$ with $\hat m$ a scale to
be defined later. Our results are generally applicable if $\tau \lesssim 1/Q$.
As already discussed in a previous paper, the transverse energy flow $S^i$ of
the gluon field exhibits hydrodynamic-like contributions that follow transverse
gradients of the energy density $\nabla^i \varepsilon$. In addition, a
rapidity-odd energy flow also emerges from the non-abelian analog of Gauss' Law
and generates non-vanishing angular momentum of the field. We will discuss the
space-time picture that emerges from our analysis and its implications for
observables in heavy ion collisions.
