Energy conditions, traversable wormholes and dust shells

TL;DR

This paper reviews energy conditions and constructs a traversable wormhole with a dust shell, demonstrating ways to minimize exotic matter and analyzing its physical and traversability properties.

Contribution

It presents a new model of a traversable wormhole with a dust shell that minimizes exotic matter and satisfies energy conditions at the junction surface.

Findings

Null and averaged null energy conditions are violated in the wormhole.

Regions with positive surface energy density are identified, satisfying energy conditions.

Estimated wormhole dimensions and traversal parameters are provided.

Abstract

Firstly, we review the pointwise and averaged energy conditions, the quantum inequality and the notion of the ``volume integral quantifier'', which provides a measure of the ``total amount'' of energy condition violating matter. Secondly, we present a specific metric of a spherically symmetric traversable wormhole in the presence of a generic cosmological constant, verifying that the null and the averaged null energy conditions are violated, as was to be expected. Thirdly, a pressureless dust shell is constructed around the interior wormhole spacetime by matching the latter geometry to a unique vacuum exterior solution. In order to further minimize the usage of exotic matter, we then find regions where the surface energy density is positive, thereby satisfying all of the energy conditions at the junction surface. An equation governing the behavior of the radial pressure across the junction surface is also deduced. Lastly, taking advantage of the construction, specific dimensions of the wormhole, namely, the throat radius and the junction interface radius, and estimates of the total traversal time and maximum velocity of an observer journeying through the wormhole, are also found by imposing the traversability conditions.