Quantifying energy condition violations in traversable wormholes

TL;DR

This paper investigates how to quantify and potentially minimize the energy condition violations in traversable wormholes using volume integrals and specific geometric constructions.

Contribution

It introduces a method to quantify the extent of energy condition violations and explores how to minimize these violations through particular geometric models.

Findings

Quantified energy condition violations using volume integrals.

Identified geometric constructions that can minimize violations.

Outlined examples and potential for reducing violations.

Abstract

The `theoretical' existence of traversable Lorentzian wormholes in the classical, macroscopic world is plagued by the violation of the well--known energy conditions of General Relativity. In this brief article we show : (i) how the extent of violation can be quantified using certain volume integrals (ii) whether this `amount of violation' can be minimised for some specific cut--and--paste geometric constructions. Examples and possibilities are also outlined.