Stress-energy tensor in the Bel-Szekeres space-time

TL;DR

This paper applies an approximation method to compute the vacuum expectation value of the stress-energy tensor in the Bel-Szekeres space-time, revealing unbounded behavior near the Cauchy horizon during electromagnetic wave collisions.

Contribution

It extends an existing approximation procedure to the Bel-Szekeres solution, providing new insights into quantum effects in colliding plane wave space-times.

Findings

Stress-energy tensor becomes unbounded near the Cauchy horizon.

Behavior matches previous results in similar non-singular space-times.

Supports the idea of quantum effects indicating singularity formation.

Abstract

In a recent work an approximation procedure was introduced to calculate the vacuum expectation value of the stress-energy tensor for a conformal massless scalar field in the classical background determined by a particular colliding plane wave space-time. This approximation procedure consists in appropriately modifying the space-time geometry throughout the causal past of the collision center. This modification in the geometry allows to simplify the boundary conditions involved in the calculation of the Hadamard function for the quantum state which represents the vacuum in the flat region before the arrival of the waves. In the present work this approximation procedure is applied to the non-singular Bel-Szekeres solution, which describes the head on collision of two electromagnetic plane waves. It is shown that the stress-energy tensor is unbounded as the killing-Cauchy horizon of the interaction is approached and its behavior coincides with a previous calculation in another example of non-singular colliding plane wave space-time.