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

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.

37 pages, LaTeX, 1 figure as a separate postscript file using uufiles. Full postscript version soon available at ftp://ftp.ifae.es/preprint/ft/uabft390.ps. A change in voffset latex command has been performed

References in corpus (8)

• Semiclassical Equations for Weakly Inhomogeneous Cosmologies
• Constant magnetic field in closed string theory: an exactly solvable model
• Four Dimensional Plane Wave String Solutions with Coset CFT Description
• Strings in Plane Wave Backgrounds Revisited
• The Master Field for QCD and $q$-Deformed Quantum Field Theory
• Planckian Energy Scattering, Colliding Plane Gravitational Waves and Black Hole Creation
• Particle creation in a colliding plane wave spacetime: wave packet quantization
• Particle Creation in the Bell-Szekeres Spacetime

Cited by in corpus (8)

• A Kinetic Theory Approach to Quantum Gravity
• Invariance of Unruh and Hawking radiation under matter-induced supertranslations
• Renormalized stress tensor in one-bubble spacetimes
• Neutrino current in a gravitational plane wave collision background
• Stress-energy tensor in colliding plane wave space-times: An approximation procedure
• Detecting the processes of colliding plane gravitational waves by electromagnetic response signals
• Some constraints for the extensions of the degenerate Ferrari and Ibanez solution
• Stress-energy tensor in the Bel-Szekeres space-time