Vacuum fluctuations for spherical gravitational impulsive waves

TL;DR

This paper introduces a method to compute vacuum fluctuations around spherical impulsive gravitational waves, yielding finite stress-energy tensor expectations by incorporating a cosmological constant and infrared parameter considerations.

Contribution

It presents a novel approach to calculate vacuum fluctuations in impulsive gravitational wave backgrounds, ensuring finiteness through a specific limiting process.

Findings

Finite vacuum expectation value of stress-energy tensor obtained

Method relies on including and then removing a cosmological constant

Infrared parameter's role in regularizing the calculation

Abstract

We propose a method for calculating vacuum fluctuations on the background of a spherical impulsive gravitational wave which results in a finite expression for the vacuum expectation value of the stress-energy tensor. The method is based on first including a cosmological constant as an auxiliary constant. We show that the result for the vacuum expectation value of the stress-energy tensor in second-order perturbation theory is finite if both the cosmological constant and the infrared parameter tend to zero at the same rate.