Casimir effect for scalar fields with Robin boundary conditions in Schwarzschild background

TL;DR

This paper calculates the vacuum stress tensor of a massless scalar field with Robin boundary conditions in a Schwarzschild background, combining Casimir effect, trace anomaly, and Hawking radiation effects.

Contribution

It provides an explicit calculation of the stress tensor incorporating boundary conditions, quantum effects, and black hole background in a two-dimensional setting.

Findings

Stress tensor expressed via Casimir effect, trace anomaly, and Hawking radiation.

Explicit formulas for vacuum expectation values in Schwarzschild background.

Insights into quantum field behavior near black hole horizons.

Abstract

The stress tensor of a massless scalar field satisfying Robin boundary conditions on two one-dimensional wall in two-dimensional Schwarzschild background is calculated. We show that vacuum expectation value of stress tensor can be obtained explicitly by Casimir effect, trace anomaly and Hawking radiation.