Traversable wormholes supported by GUP corrected Casimir energy
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Regular Article - Theoretical Physics
Traversable wormholes supported by GUP corrected Casimir energy Kimet Jusufi1,2,a , Phongpichit Channuie3,4,5,6,b , Mubasher Jamil7,8,c 1
Physics Department, State University of Tetovo, Ilinden Street nn, 1200 Tetovo, Macedonia Institute of Physics, Faculty of Natural Sciences and Mathematics, Ss. Cyril and Methodius University, Arhimedova 3, 1000 Skopje, Macedonia 3 School of Science, Walailak University, Thasala, Nakhon Si Thammarat 80160, Thailand 4 College of Graduate Studies, Walailak University, Thasala, Nakhon Si Thammarat 80160, Thailand 5 Research Group in Applied, Computational and Theoretical Science (ACTS), Walailak University, Thasala, Nakhon Si Thammarat 80160, Thailand 6 Thailand Center of Excellence in Physics, Ministry of Education, Bangkok 10400, Thailand 7 Institute for Theoretical Physics and Cosmology, Zhejiang University of Technology, Hangzhou 310023, China 8 Department of Mathematics, School of Natural Sciences (SNS), National University of Sciences and Technology (NUST), H-12, Islamabad 44000, Pakistan
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Received: 30 December 2019 / Accepted: 25 January 2020 © The Author(s) 2020
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 Pr (r ) = ωr (r )ρ(r ) and Pt (r ) = ωt (r )Pr (r ) 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 r0 , 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.
1 Introduction The search for a theory of exotic objects through Einstein’s general theory of relativity has received a lot of interest in the a e-mail:
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literature. A black hole, e.g. the Schwarzschild black hole, possesses one of the possible solutions to Einstein’s field equations; see Ref. [1]. The recent detection of gravitational waves (GWs) [2] demonstrated that stellar-mass black holes really exist in Nature. Interestingly, the author of Ref. [3] realized in 1916 that another solution was viable which is presently known as a “white
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