Static and dynamic traversable wormhole geometries satisfying the Ford-Roman constraints

TL;DR

This paper explores both static and dynamic wormhole solutions that satisfy Ford-Roman quantum constraints, analyzing their energy conditions and traversability, and demonstrating the challenges in avoiding weak energy condition violations.

Contribution

It provides a broad class of wormhole geometries meeting quantum constraints and examines their properties, including static and dynamic cases, with detailed analysis of energy conditions.

Findings

Static wormholes satisfying Ford-Roman constraints identified

Dynamic wormholes likely violate weak energy condition temporarily

Traversability criteria are analyzed in relation to quantum constraints

Abstract

It was shown by Ford and Roman in 1996 that quantum field theory severely constrains wormhole geometries on a macroscopic scale. The first part of this paper discusses a wide class of wormhole solutions that meet these constraints. The type of shape function used is essentially generic. The constraints are then discussed in conjunction with various redshift functions. Violations of the weak energy condition and traversability criteria are also considered. The second part of the paper analyzes analogous time-dependent (dynamic) wormholes with the aid of differential forms. It is shown that a violation of the weak energy condition is not likely to be avoidable even temporarily.