Oliveira and colleagues carried out study on the existence of Traversable Casimir Wormholes in arbitrary dimensions. They showed that, Casimir energy can be a source of the Morris-Thorne wormhole for all spacetime dimensions (D) greater than 3. Their study recently appeared in Arxiv.
In 2019, Garattini showed that, in four dimensions, only the standard negative Casimir energy density and the radial pressure are able to form a Morris-Thorne Wormhole. On another hand, in a recent paper, Alencar and colleagues showed that in three dimensions the same is not true, thus, this inspired Oliveira and colleagues to investigate the influence of dimensionality of spacetime on the Casimir wormhole, in order to generalize both results.
In order to investigate the influence, they first analyzed Einstein’s equation in D dimensions static and spherically symmetric spacetime and considered the Casimir energy and pressure as sources. They found that the solution depends only on the redshift and shape functions.
They also showed that the boundary and flare-out conditions can be satisfied for any dimensions. Therefore, these conditions do not impose any restrictions for Casimir wormholes in D dimensions.
In addition, it has been shown, why for 3D spacetimes it is not possible to form wormholes. They showed it, by obtaining a general condition which was satisfied by the state parameter wD. It is given by
This expression revealed that for D= 3 we must have w3 = 0, this eliminates the possibility of Casimir source and thus, the formation of wormhole in 3D spacetimes.
Finally, by computing the integrand (Φ(r)), they showed that, for every spacetime of dimension greater than 3, it is possible to construct a traversable Morris-Thorne wormhole by using casimir energy as a source.
“We should point that this must have consequences for the physics of extra dimensions, particularly related to the newly discover humanly traversable wormhole. It would be interesting to generalize the above result to backgrounds that are not asymptotically flat. This is the topic of our future works.”— concluded authors of the study
Reference: P.H.F. Oliveira, G. Alencar, I.C. Jardim, R.R. Landim, “Traversable Casimir Wormholes in D Dimensions”, Arxiv, pp. 1-6, 2021.
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