Casimir Wormholes in (2+1) Dimensions with Applications to the Graphene

TL;DR

This paper investigates the limitations of forming wormholes in (2+1) dimensions using Casimir energy, showing that additional factors like a cosmological constant and magnetic fields are needed, and explores potential graphene analogs.

Contribution

It demonstrates that Casimir energy alone cannot source (2+1)D wormholes, unlike in 4-D, and proposes methods to overcome this limitation, including embedding in higher dimensions and magnetic fields.

Findings

Casimir energy alone cannot form (2+1)D wormholes.

Introducing a cosmological constant and magnetic fields enables wormhole formation.

Potential realization of wormholes in graphene with electronic transport analysis.

Abstract

In this paper we show that wormholes in (2+1) dimensions (3-D) cannot be sourced solely by both Casimir energy and tension, differently from what happens in a 4-D scenario, in which case it has been shown recently, by the direct computation of the exact shape and redshift functions of a wormhole solution, that this is possible. We show that in a 3-D spacetime the same is not true since the arising of at least an event horizon is inevitable. We do the analysis for massive and massless fermions, as well as for scalar fields, considering quasi-periodic boundary conditions and find that a possibility to circumvent such a restriction is to introduce, besides the 3-D Casimir energy density and tension, a cosmological constant, embedding the surface in a 4-D manifold and applying a perpendicular weak magnetic field. This causes an additional tension on it, which contributes to the formation of the wormhole. Finally, we discuss the possibility of producing the condensed matter analogous of this wormhole in a graphene sheet and analyze the electronic transport through it.