Surface stresses on a thin shell surrounding a traversable wormhole

TL;DR

This paper analyzes the surface stresses on a thin shell surrounding a traversable wormhole, matching interior and exterior solutions, and explores conditions for energy compliance and physical properties of the shell.

Contribution

It provides a detailed analysis of surface stresses and energy conditions on a thin shell in a traversable wormhole spacetime, including the effects of a cosmological constant.

Findings

Regions where weak and null energy conditions are satisfied are identified.

Surface pressure can be positive or negative depending on parameters.

An equation for radial pressure behavior across the junction is derived.

Abstract

We match an interior solution of a spherically symmetric traversable wormhole to a unique exterior vacuum solution, with a generic cosmological constant, at a junction interface, and the surface stresses on the thin shell are deduced. In the spirit of minimizing the usage of exotic matter we determine regions in which the weak and null energy conditions are satisfied on the junction surface. The characteristics and several physical properties of the surface stresses are explored, namely, regions where the sign of the tangential surface pressure is positive and negative (surface tension) are determined. This is done by expressing the tangential surface pressure as a function of several parameters, namely, that of the matching radius, the redshift parameter, the surface energy density and of the generic cosmological constant. An equation governing the behavior of the radial pressure across the junction surface is also deduced.