https://doi.org/10.1140/epjc/s10052-021-09734-0
Regular Article - Theoretical Physics
Casimir wormholes in 
dimensions with applications to the graphene
1
Universidade Federal do Ceará, Fortaleza, CE, Brazil
2
International Institute of Physics, Federal University of Rio Grande do Norte, Campus Universitário, Lagoa Nova, 59078-970, Natal, RN, Brazil
3
Departamento de Física, Universidade Federal da Paraíba, João Pessoa, PB, Brazil
4
Universidade Estadual do Ceará, Faculdade de Educação, Ciências e Letras de Iguatu, Iguatu, CE, Brazil
Received:
19
May
2021
Accepted:
10
October
2021
Published online:
20
October
2021
In this paper we show that wormholes in (2+1) dimensions (3-D) cannot be sourced solely by both Casimir energy density 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.
© The Author(s) 2021
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