Quantum Inequalities for the Electromagnetic Field

TL;DR

This paper derives a quantum inequality for the electromagnetic field in static curved spacetimes, providing a generalized expression applicable to various geometries and sampling functions, with specific examples in Minkowski, Rindler, and Einstein universes.

Contribution

It introduces a generalized quantum inequality for the electromagnetic field in static curved spacetimes using mode function expansion and arbitrary sampling functions.

Findings

Quantum inequality formulated for static curved spacetimes.

Explicit examples provided for Minkowski, Rindler, and Einstein universes.

Flexible sampling functions with positivity, continuity, and decay constraints.

Abstract

A quantum inequality for the quantized electromagnetic field is developed for observers in static curved spacetimes. The quantum inequality derived is a generalized expression given by a mode function expansion of the four-vector potential, and the sampling function used to weight the energy integrals is left arbitrary up to the constraints that it be a positive, continuous function of unit area and that it decays at infinity. Examples of the quantum inequality are developed for Minkowski spacetime, Rindler spacetime and the Einstein closed universe.