Gravitational shock waves and vacuum fluctuations

TL;DR

This paper investigates the behavior of vacuum fluctuations in the presence of spherical gravitational shock waves, revealing divergences at second order perturbation theory and highlighting differences from impulsive waves.

Contribution

It demonstrates that the vacuum expectation value of the stress-energy tensor diverges at second order for spherical shock waves, unlike impulsive waves, indicating a qualitative difference in their quantum effects.

Findings

Vacuum expectation value diverges at second order for spherical shock waves.

No infrared divergences are observed at second order.

Qualitative differences exist between shock and impulsive wave solutions.

Abstract

We show that the vacuum expectation value of the stress-energy tensor of a scalar particle on the background of a spherical gravitational shock wave does not give a finite expression in second order perturbation theory, contrary to the case seen for the impulsive wave. No infrared divergences appear at this order. This result shows that there is a qualitative difference between the shock and impulsive wave solutions which is not exhibited in first order.