Accounting for exotic matter and the extreme radial tension in Morris-Thorne wormholes of embedding class one

TL;DR

This paper explores Morris-Thorne wormholes within five-dimensional embedding class one spacetimes, focusing on the origin of exotic matter and the extreme radial tension at the throat, using a timelike fifth dimension.

Contribution

It introduces a novel approach by embedding wormholes in five-dimensional spacetime with a timelike extra dimension, addressing exotic matter and tension issues.

Findings

Exotic matter's origin is linked to higher-dimensional embedding.

Radial tension at the wormhole throat is explained via embedding properties.

Embedding class one spacetime offers new insights into wormhole stability.

Abstract

The embedding of a curved spacetime in a higher-dimensional flat spacetime has continued to be a topic of interest in the general theory of relativity, as exemplified by the induced-matter theory. This paper deals with spacetimes of embedding class one, i.e., spacetimes that can be embedded in a five-dimensional flat spacetime. Einstein's theory allows the fifth dimension to be either spacelike or timelike. By assuming the latter, this paper addresses two fundamental issues concerning Morris-Thorne wormholes, the origin of exotic matter and the frequently inexplicable enormous radial tension at the throat.