Vacuum polarization around a three-dimensional black hole

TL;DR

This paper computes the vacuum polarization effects of a conformally coupled scalar field around a three-dimensional black hole, providing insights into quantum field behavior in curved spacetime.

Contribution

It presents the first calculation of the Euclidean propagator and the expectation value of the field squared in this specific black hole background.

Findings

Calculated the Euclidean propagator for the scalar field.

Derived the expectation value of $ angle ext{ extbackslash varphi}^2 angle$ in the Hartle-Hawking state.

Enhanced understanding of quantum effects near three-dimensional black holes.

Abstract

We calculate the Euclidean propagator for a conformally coupled massless scalar field in the background of the three-dimensional black hole. The expectation value $\langle\varphi^2\rangle$ in the Hartle-Hawking state is obtained in the spacetime.