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.
Highlights
Wormholes are handles or tunnels in spacetime connecting widely separated regions of our Universe or different universes in a multiverse
Returning to the induced-matter theory, since the vacuum field equations in five dimensions yield the Einstein field equations with matter, one could argue that matter is geometric in origin: what we perceive as matter is the impingement of the fifth dimension onto our spacetime; this would include exotic matter
Embedding theorems have continued to be a topic of interest in the general theory of relativity, as exemplified by the induced-matter theory
Summary
Wormholes are handles or tunnels in spacetime connecting widely separated regions of our Universe or different universes in a multiverse. [1] that the Einstein field equations can be rearranged to yield τ : reintroducing c and G for this is given by τ (r ) From this condition it follows that the radial tension at the throat is τ (r0) =. For r0 = 3 km, τ (r ) has the same magnitude as the pressure at the center of a massive neutron star [1] Attributing this outcome to exotic matter makes little sense, given that exotic matter was introduced to ensure a violation of the NEC. Dark matter can in principle support traversable wormholes due to the NEC violation [6,7], but the extremely low energy density cannot account for the large radial tension.
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