In this paper the averaged weak and averaged null 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. © 1996 The American Physical Society.

• Received 23 June 1995

DOI:https://doi.org/10.1103/PhysRevD.53.1988