Flare-out condition of Morris-Thorne wormhole and finiteness of pressure

TL;DR

This paper revisits the flare-out condition of Morris-Thorne wormholes, analyzing the Einstein equations to understand the finiteness of pressure and its physical implications for maintaining the wormhole structure.

Contribution

It provides a re-examination of the flare-out condition using Einstein's equations and explores the physical meaning of pressure finiteness in wormhole stability.

Findings

Finiteness of pressure at the wormhole throat is physically significant.

The flare-out condition relates to large surface tension compared to energy density.

Re-analysis clarifies the physical interpretation of wormhole stability conditions.

Abstract

Wormhole is defined as the topological structure with the throat connecting two asymptotically flat spaces. In order to have and maintain the structure of the wormhole, there needs the geometrical flare-out condition, i.e., the minimal size at throat. In the case of Morris-Thorne type wormhole, the condition is given by the huge surface tension compared to the energy density times the square of the light speed. In this paper, we re-considered the flare-out condition for the wormhole with the Einstein equation, checked the finiteness of the pressure, and investigated its physical meaning.