Quantum elds interacting with colliding plane waves: the stress-energy tensor and backreaction

Following a previous work on the quantization of a massless scalar eld in a space-time representing the head on collision of two plane waves which fucus into a Killing-Cauchy horizon, we compute the renormalized expectation value of the stress-energy tensor of the quantum eld near that horizon in the physical state which corresponds to the Minkowski vacuum before the collision of the waves. It is found that for minimally coupled and conformally coupled scalar elds the respective stress-energy tensors are unbounded in the horizon. The speciic form of the divergences suggests that when the semiclassical Einstein equations describing the backreaction of the quantum elds on the spacetime geometry are taken into account, the horizon will acquire a curvature singularity. Thus the Killing-Cauchy horizon which is known to be unstable under \generic" classical perturbations is also unstable by vacuum polarization. The calculation is done following the point splitting regularization technique. The dynamical colliding wave spacetime has four quite distinct spacetime regions, namely, one at region , two single plane wave regions, and one interaction region. Exact mode solutions of the quantum eld equation cannot be found exactly, but the blueshift suuered by the initial modes in the plane wave and interaction regions makes the use of the WKB expansion a suitable method of solution. To ensure the correct regularization of the stress-energy tensor, the initial at modes propagated into the interaction region must be given to a rather high adiabatic order of approximation.