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

TL;DR

This paper investigates the quantum stress-energy tensor near the horizon formed by colliding plane waves, revealing divergences that imply the horizon becomes a curvature singularity when quantum backreaction is considered.

Contribution

It provides a detailed calculation of the renormalized stress-energy tensor in a colliding plane wave spacetime, showing the horizon's instability due to quantum effects.

Findings

Stress-energy tensor diverges at the horizon for scalar fields.

Quantum backreaction likely turns the horizon into a singularity.

Horizon instability extends from classical to quantum perturbations.

Abstract

Following a previous work on the quantization of a massless scalar field in a spacetime 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 field 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 fields the respective stress-energy tensors are unbounded in the horizon. The specific form of the divergences suggests that when the semiclassical Einstein equations describing the backreaction of the quantum fields 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 flat region, two single plane wave regions, and one interaction region. Exact mode solutions of the quantum field equation cannot be found exactly, but the blueshift suffered 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 flat modes propagated into the interaction region must be given to a rather high adiabatic order of approximation.