The Average Null Energy Condition for Classical Dirac Fields*

Assessing whether known matter fields satisfy or violate energy conditions is of central importance — both for theoretical results in general relativity, and for restricting the class of physically allowed spacetimes, such as traversable wormholes. Though it is understood that quantum fields violate all pointwise energy conditions, there is hope that the averaged version of the null energy condition (ANEC) may hold true generically. In this talk, I will discuss recent progress towards whether ANEC holds for the Dirac field, by discussing to what extent this energy condition is respected by positive frequency classical Dirac fields in static, spherically symmetric spacetimes. This problem is an important first step towards determining whether a general, quantum Dirac field should satisfy ANEC. In particular, I will assess the whether solutions to the Dirac equations could conceivably generate the “negative energy” required to support the viability of static, spherically symmetric wormholes.