Null second order corrections to Casimir energy in weak gravitational field: The Schwinger's approach

TL;DR

This paper demonstrates that in a static weak gravitational field, the Casimir energy for a massless scalar field with Dirichlet boundaries remains unchanged from its flat space-time value, using Schwinger's approach.

Contribution

It shows that gravitational corrections to Casimir energy vanish in weak static fields, challenging previous findings of such effects.

Findings

Casimir energy remains unaltered in weak gravitational fields

Results are consistent across a general class of backgrounds

Implications for earlier studies claiming gravity-related corrections

Abstract

We show through Schwinger's approach that in a static weak gravitational background, the Casimir Energy for a real massless scalar field obeying Dirichlet boundary conditions on rectangular plates is unaltered from it's flat space-time value. The result is obtained considering an rather general class of backgrounds, adding further generality and consistency test for the previous work. The proposed result has direct consequences on earlier works in the literature that found gravity related corrections for similar setups.