Generic wormhole throats

Wormholes and black holes have, apart from a few historical oddities, traditionally been treated a quite separate objects with relatively little overlap. The possibility of a connection arises in that wormholes, if they exist, might have profound influence on black holes, their event horizons, and their internal structure. For instance: (1) small wormhole-induced perturbations in the geometry can lead to massive non-perturbative shifts in the event horizon, (2) Planck-scale wormholes near any spacelike singularity might let information travel in effectively spacelike directions, (3) vacuum polarization effects near any singularity might conceivably lead to a “punch through” into another asymptotically flat region—effectively transforming a black hole into a wormhole. After discussing these connections between black hole physics and wormhole physics we embark on an overview of what can generally be said about traversable wormholes and their throats. We discuss the violations of the energy conditions that typically occur at and near the throat of any traversable wormhole and emphasize the generic nature of this result. We discuss the original Morris–Thorne wormhole and its generalization to a spherically symmetric