Casimir effect in the curved background and the black hole in three dimensions

TL;DR

This paper studies the quantum correction to the Casimir effect in a three-dimensional curved background with a periodic coordinate, revealing how quantum effects alter black hole geometry to resemble a Reissner-Nordström solution.

Contribution

It introduces a method to compute quantum corrections to the Casimir energy in curved 3D backgrounds and analyzes their impact on black hole geometry.

Findings

Quantum correction modifies the black hole geometry.

The corrected geometry resembles the Reissner-Nordström solution.

The correction term is expressed as an expansion of the metric.

Abstract

We consider the quantum correction to the Lagrangean by the massless free boson in the curved background in three dimensions where one of the coordinates is periodic. The correction term is given by an expansion of the metric with respect to the derivative and the first term expresses to the usual Casimir energy. As an application, we investigate the change of the geometry in three dimensional black hole due to the quantum effect and we show that the geometry becomes like that of the Reissner-Nordstr\o m solution.