  In a recent work on the quantization of a massless scalar field in a
particular colliding plane wave space-time, we computed the vacuum expectation
value of the stress-energy tensor on the physical state which corresponds to
the Minkowski vacuum before the collision of the waves. We did such a
calculation in a region close to both the Killing-Cauchy horizon and the
folding singularities that such a space-time contains. In the present paper, we
give a suitable approximation procedure to compute this expectation value, in
the conformal coupling case, throughout the causal past of the center of the
collision. This will allow us to approximately study the evolution of such an
expectation value from the beginning of the collision until the formation of
the Killing-Cauchy horizon. We start with a null expectation value before the
arrival of the waves, which then acquires nonzero values at the beginning of
the collision and grows unbounded towards the Killing-Cauchy horizon. The value
near the horizon is compatible with our previous result, which means that such
an approximation may be applied to other colliding plane wave space-times. Even
with this approximation, the initial modes propagated into the interaction
region contain a function which cannot be calculated exactly and to ensure the
correct regularization of the stress-energy tensor with the point-splitting
technique, this function must be given up to adiabatic order four of
approximation.
