Traversable wormholes: minimum violation of null energy condition revisited

TL;DR

This paper revisits the conditions for traversable wormholes, demonstrating that minimizing exotic matter either results in a horn or infinite stresses at the throat, challenging previous assumptions about small violations of null energy conditions.

Contribution

It provides a detailed analysis showing that reducing exotic matter near the wormhole throat inevitably leads to a horn or infinite stresses, refining the understanding of wormhole stability.

Findings

Minimizing exotic matter leads to a horn instead of a wormhole.

Approaching the horizon causes infinite stresses at the throat.

Small violations of null energy conditions are insufficient for stable traversable wormholes.

Abstract

It was argued in literature that traversable wormholes can exist with arbitrarily small violation of null energy conditions. We show that if the amount of exotic material near the wormhole throat tends to zero, either this leads to a horn instead of a wormhole or the throat approaches the horizon in such a way that infnitely large stresses develop on the throat.