No time machine on the cheap: why semiclassical wormholes won’t do

Abstract

If you can control a wormhole, you can time-travel. The issue is whether they can exist at all. Wormhole solutions in general relativity have spectacular local and global features. Invariantly, a wormhole throat is an outer marginally trapped surface satisfying additional constraints. Some of its properties — like violation of the energy conditions — it shares with black holes that are required to trap light in finite time for a distant observer. This condition may be contentious for black and white holes, but it is the essential part of what “traversable” means. Standard traversable wormholes, such as those described by the Ellis-Morris-Thorne or Simpson-Visser metrics, are static and spherically symmetric. We show that no dynamical solution of the semiclassical Einstein equations can asymptote to these geometries. Conversely, dynamical solutions that do exist either fail to yield a traversable static limit, or breach quantum energy inequalities that bound violations of the null energy condition, or lead to divergent tidal forces. These conclusions hold independently of the choice of quantum fields. Such symmetric wormholes, therefore, are ruled out in semiclassical gravity — making time travel a costlier proposition.