Traversable wormholes supported by GUP corrected Casimir energy

Abstract In this paper, we investigate the effect of the Generalized Uncertainty Principle (GUP) in the Casimir wormhole spacetime recently proposed by Garattini (Eur Phys J C 79: 951, 2019). In particular, we consider three types of GUP relations, firstly the Kempf, Mangano and Mann (KMM) model, secondly the Detournay, Gabriel and Spindel (DGS) model, and finally the so-called type II model for the GUP principle. To this end, we consider three specific models of the redshift function along with two different equations of state (EoS), given by $${\mathcal {P}}_r(r)=\omega _r(r) \rho (r)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mi>r</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>r</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mi>ω</mml:mi><mml:mi>r</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>r</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mi>ρ</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>r</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math> and $${\mathcal {P}}_t(r)=\omega _t (r){\mathcal {P}}_r(r)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mi>t</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>r</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mi>ω</mml:mi><mml:mi>t</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>r</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mi>r</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>r</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math> and obtain a class of asymptotically flat wormhole solutions supported by Casimir energy under the effect of GUP. Furthermore we check the null, weak, and strong condition at the wormhole throat with a radius $$r_0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>r</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:math> , and we show that in general the classical energy conditions are violated by some arbitrary quantity at the wormhole throat. Importantly, we examine the wormhole geometry with semiclassical corrections via embedding diagrams. We also consider the ADM mass of the wormhole, the volume-integral quantifier to calculate the amount of the exotic matter near the wormhole throat, and the deflection angle of light.

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