Averaged Energy Conditions and Evaporating Black Holes

TL;DR

This paper investigates averaged energy conditions and quantum inequalities in evaporating black hole spacetimes, analyzing where violations occur and their implications for singularity theorems.

Contribution

It extends the analysis of averaged energy conditions and quantum inequalities to evaporating black holes in both 2D and 4D, focusing on half-geodesic integrals and violation regions.

Findings

Averaged energy conditions are violated in certain regions of evaporating black hole spacetimes.

Quantum inequalities bound the negative energy magnitude and extent during violations.

Results have implications for the validity of singularity theorems in such spacetimes.

Abstract

In this paper the averaged weak (AWEC) and averaged null (ANEC) energy conditions, together with uncertainty principle-type restrictions on negative energy (``quantum inequalities''), are examined in the context of evaporating black hole backgrounds in both two and four dimensions. In particular, integrals over only half-geodesics are studied. We determine the regions of the spacetime in which the averaged energy conditions are violated. In all cases where these conditions fail, there appear to be quantum inequalities which bound the magnitude and extent of the negative energy, and hence the degree of the violation. The possible relevance of these results for the validity of singularity theorems in evaporating black hole spacetimes is discussed.