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

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.