$<\phi^2>$ in the Spacetime of a Cylindrical Black Hole

TL;DR

This paper calculates the renormalised <phi^2> for a scalar field in a cylindrical black hole spacetime, revealing its behavior near the horizon, as a step towards understanding back reaction effects in such geometries.

Contribution

It provides the first calculation of <phi^2> in a cylindrical black hole spacetime with a conformally coupled scalar field, advancing the study of quantum effects in these geometries.

Findings

<phi^2> is divergence free throughout the spacetime.

<phi^2> attains its maximum near the horizon.

Abstract

The renormalised value of $<\phi^2>$ is calculated for a massless, conformally coupled scalar field in the Hartle-Hawking vacuum state. This calculation is a first step towards the calculation of the gravitational back reaction of the field in a black cosmic string spacetime which is asymptotically anti-DeSitter and possesses a non constant dilaton field. It is found that the field is divergence free throughout the spacetime and attains its maximum value near the horizon.