Wormholes (WHs) require negative energy, and therefore an exotic matter source. Since Casimir energy is negative, it has been speculated as a good candidate to source those objects a long time ago. However, only very recently, a full solution for [Formula: see text] has been found by [R. Garattini, Eur. Phys. J. C 79, 951 (2019), doi:10.1140/epjc/s10052-019-7468-y] thus the Casimir energy can be a source of traversable WHs. Soon later [G. Alencar, V. B. Bezerra and C. R. Muniz, arXiv:2104.13952 [gr-qc]] have shown, that this is not true in [Formula: see text]. In this paper, we show that Casimir energy can be a source of the Morris–Thorne WH for all spacetime with [Formula: see text]. Finally, we add the cosmological constant and find that for [Formula: see text] Casimir WHs are possible, however, the space must always be AdS. For [Formula: see text], we show that the cosmological constant invert the signal with increasing throat size.

Wormholes require negative energy, and therefore an exotic matter source. Since Casimir’s energy is negative, it has been speculated as a good candidate to source those objects a long time ago. However, only very recently a full solution for 3+1 dimensions has been found by Garattini, thus the Casimir energy can be a source of traversable wormholes. We have recently shown that this can be generalized to higher dimensional spacetimes. Lately, Garattini sought to analyze the effects of Yukawa-type terms on shape functions and obtained promising results. However, his approach breaks down the usual relation between the energy density and the radial pressure of the Casimir field. In this work, we study the effects of the same three Yukawa-type corrective factors on the shape function of the Casimir wormhole keeping the usual way to obtain the radial pressure from the energy density. We show that, in addition to being able to construct traversable wormholes that satisfy all the necessary conditions, it is possible to obtain adequate constraints on the constants to recover the standard case with no double limit used by Garatinni. We show that, for some values of the Yukawa parameter, it is possible to generate a repulsive gravitational wormhole. Finally, we analyze the stability of the solutions and find the upper bounds for the Yukawa factor.

Resumo Nesse trabalho, analisamos de maneira crítica as peculiaridades e potencialidades de três abordagens para o cálculo das forças de vínculo em sistemas clássicos holônomos, a saber, o formalismo Newtoniano, o formalismo Lagraniano e um terceiro método misto desenvolvido pelo físico brasileiro Nivaldo A. Lemos [1]. Analisando as soluções de três problemas clássicos por cada um desses métodos, concluímos que o número de dimensões e a quantidade de vínculos do problema influem sobre a eficiência dos métodos, o que proporcionou o estabelecimento de um critério para a escolha do formalismo a ser utilizado.

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