Wormhole restrictions from quantum energy inequalities

TL;DR

This paper reviews how quantum energy inequalities impose restrictions on the existence and properties of traversable wormholes in semiclassical gravity, including new constraints on certain long wormhole solutions.

Contribution

It provides a comprehensive review of quantum energy inequalities' impact on wormhole physics and introduces new constraints on long wormholes using the doubled smeared null energy condition.

Findings

QEIs restrict the construction of traversable wormholes.

Both short and long wormholes are examined under these constraints.

A new constraint on long wormholes from the doubled smeared null energy condition is presented.

Abstract

Wormhole solutions, bridges that connect different parts of spacetime, were proposed early in the history of General Relativity. Soon after, it was shown that all wormholes violate classical energy conditions, which are non-negativity constraints on contractions of the stress-energy tensor. Since these conditions are violated by quantum fields, it was believed that wormholes can be constructed in the context of semiclassical gravity. But negative energies in quantum field theory are not without restriction: quantum energy inequalities (QEIs) control renormalized negative energies averaged over a geodesic. Thus, QEIs provide restrictions on the construction of wormholes. This work is a review of the relevant literature, thus focusing on results where QEIs restrict traversable wormholes. Both 'short' and 'long' (without causality violations) wormhole solutions in the context of semiclassical gravity are examined. A new result is presented on constraints on the Maldacena, Milekhin, and Popov 'long' wormhole from the recently derived doubled smeared null energy condition.