Averaged Energy Conditions in 4D Evaporating Black Hole Backgrounds

TL;DR

This paper investigates averaged energy conditions in 4D evaporating black hole backgrounds using a semi-analytical model, revealing quantum inequalities that bound negative energy where classical conditions fail.

Contribution

It provides a detailed analysis of energy conditions and quantum inequalities in evaporating black hole spacetimes, extending understanding of negative energy constraints.

Findings

Averaged weak and null energy conditions are violated in some regions.

Quantum inequalities impose bounds on negative energy magnitude and duration.

Results support the consistency of quantum field theory with black hole evaporation models.

Abstract

Using Visser's semi-analytical model for the stress-energy tensor corresponding to the conformally coupled massless scalar field in the Unruh vacuum, we examine, by explicitly evaluating the relevant integrals over half-complete geodesics, the averaged weak (AWEC) and averaged null (ANEC) energy conditions along with Ford-Roman quantum inequality-type restrictions on negative energy in the context of four dimensional evaporating black hole backgrounds. We find that in all cases where the averaged energy conditions fail, there exist quantum inequality bounds on the magnitude and duration of negative energy densities.