Inaccessibility of traversable wormholes

Wormhole solutions to the equations of general relativity have some spectacular local and global properties. As these unusual features are not explicitly forbidden by known physics, wormholes are considered in various astrophysical and cosmological scenarios. The paradigmatic traversable wormhole models are described by static spherically symmetric Ellis-Morris-Thorne and Simpson-Visser metrics. We show that no dynamical solution of the semiclassical Einstein equations can have these metrics as their static limit. On the other hand, possible static limits of the dynamical solutions are not traversable. Moreover, they lead to violation of a quantum energy inequality that bounds violations of the null energy condition by quantum fields. This conclusion does not depend on specific properties of fields that may be proposed for wormhole construction. As a result, spherically symmetric wormholes cannot exist in semiclassical gravity.