A model of traversable wormhole in an extended gravity theory has been proposed. The Casimir effect and Generalised Uncertainty Principle (GUP) arising out of the concept of minimal length have been considered to obtain the shape function, radial and tangential pressure of the wormhole. The effects of the GUP parameter and the parameter of the extended gravity theory on the wormhole properties have been discussed. The energy condition violation by the exotic matter of Casimir wormhole have been shown. Also we have calculated the exotic matter content of the Casimir wormhole that violate the null energy condition.
In this work, we consider a Yukawa modification of the Casimir wormhole. With the help of an Equation of State, we impose Zero Tidal Forces. We will examine two different approaches: in a first approach, we will fix the form of the shape function of the Casimir wormholes modified by a Yukawa term in three different ways and finally a superposition of different profiles. In the second approach, we will consider the original Casimir source modified by a Yukawa term in three different ways and we will deduce the form of the shape function In both the approaches the reference energy density will b…
In this work, we explore the connection between Casimir energy and an Absurdly Benign Traversable Wormhole, which in the literature has been considered only in the pioneering paper of Morris and Thorne. To have consistency with the Casimir source, we need to generalize the idea of an Absurdly Benign Traversable Wormhole into a Generalized Absurdly Benign Traversable Wormhole. With this generalization, we have found that the wormhole throat is not more Planckian, but huge. Three profiles have been studied: one of them is directly connected with the Casimir source, while the other two have been …
Casimir energy is always indicated as a potential source to generate a Traversable Wormhole. It is also used to proof the existence of negative energy which can be built in the laboratory. However, in the scientific literature there is no trace of the consequences on the traversable wormhole itself. In this work, we would like to consider such a source to see if and which kind of traversable wormhole can be produced. As a further analysis, we examine also the consequences of Quantum Weak Energy Conditions on the traversability of the wormhole. We find that an agreement with the original Casimi…
Bra-ket wormholes are non-trivial saddles in Euclidean gravity. They have to be sustained by negative Casimir energy of matter fields inside the throat. However, Casimir energy is very sensitive to boundary conditions and in presence of gauge symmetries one has to integrate over all possible boundary conditions for the matter fields, as they are a part of bra-ket wormhole moduli. For non- Abelian gauge groups the corresponding measure for the boundary conditions, which we call Casimir entropy, is non-trivial and it competes with the Casimir energy. We find that for large gauge groups this sign…
In recent years there has been a growing interest in the field of Casimir wormhole. In classical general relativity (GR), it is known that the null energy condition (NEC) has to be violated to have a wormhole to be stable. The Casimir effect is an experimentally verified effect that is caused due to the vacuum field fluctuations in quantum field theory. Since the Casimir effect provides the negative energy density, thus this act as an ideal candidate for the exotic matter needed for the stability of the wormhole. In this paper, we study the Casimir effect on the wormhole geometry in modified s…
We consider the Casimir effect for quantized massive scalar field with non-conformal coupling $ξ$ in a spacetime of wormhole whose throat is rounded by a spherical shell. In the framework of zeta-regularization approach we calculate a zero point energy of scalar field. We found that depending on values of coupling $ξ$, a mass of field $m$, and/or the throat's radius $a$ the Casimir force may be both attractive and repulsive, and even equals to zero.
In this paper, we investigate new exact and analytic solutions of the Einstein Maxwell field equations describing Casimir wormholes with and without the effect of the Generalized Uncertainty Principle (GUP). We consider a specific type of the GUP relations and study three specific models of the redshift function along with two different EoS of state. Here we obtain a class of asymptotically flat Casimir wormhole solutions with and without GUP corrections under the effect of electric charge. Furthermore we check the null, weak, strong and dominant energy conditions at the wormhole throat of rad…
Wormholes (WH) require negative energy, and therefore an exotic matter source. Since Casimir energy is negative, it has been speculated as a good candidate to source that objects a long time ago. However only very recently a full solution for D = 4 has been found by Garattini [1], thus the Casimir energy can be a source of traversable WHs. Soon later Alencar et al [2] have shown, that this is not true in D = 3. In this paper, we show that Casimir energy can be a source of the Morris-Thorne WH for all spacetime with D > 3. Finally, we add the cosmological constant and find that for D = 3 Casimi…
In this paper, we calculate the weak deflection angle by Casimir wormhole and its shadow. To do so, we derive the Gaussian optical curvature and use the Gauss-Bonnet theorem. Then we find the deflection angle by Casimir wormhole in weak field limits. Moreover, we obtain the weak deflection angle in the presence of plasma medium and see the effect of the plasma medium on the weak deflection angle. Moreover, we study a shadow of Casimir wormhole and we plot and discuss them. We show the shadow of Casimir wormhole's behavior when changing the value of $a$.
In this work we construct traversable wormholes geometries in the framework of the complexity factor. We provide the redshift function of a Casimir traversable wormhole which, in combination with a non--vanishing complexity factor, leads to a traversable wormhole with a minimum amount of exotic matter. The shape function and the embedding diagram are shown and discussed. The tidal accelerations and the time required to get through the wormholes are estimated.
In this paper, we investigate the gravitational bending angle due to the Casimir wormholes, which consider the Casimir energy as the source. Furthermore, some of these Casimir wormholes regard Generalized Uncertainty Principle (GUP) corrections of Casimir energy. We use the Ishihara method for the Jacobi metric, which allows us to study the bending angle of light and massive test particles for finite distances. Beyond the uncorrected Casimir source, we consider many GUP corrections, namely: the Kempf, Mangano and Mann (KMM) model, the Detournay, Gabriel and Spindel (DGS) model, and the so-call…
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 possibil…
In the context of a model of space-time foam, made by $N$ wormholes we discuss the possibility of having a foam formed by different configurations. An equivalence between Schwarzschild and Schwarzschild-Anti-de Sitter wormholes in terms of Casimir energy is shown. An argument to discriminate which configuration could represent a foamy vacuum coming from Schwarzschild black hole transition frequencies is used. The case of a positive cosmological constant is also discussed. Finally, a discussion involving charged wormholes leads to the conclusion that they cannot be used to represent a ground st…
We calculate the Casimir energy-momentum tensor induced in a scalar field by a macroscopic ultrastatic spherically-symmetric long-throated traversable wormhole, and examine whether this exotic matter is sufficient to stabilise the wormhole itself. The Casimir energy-momentum tensor is obtained (within the $\mathbb{R}\times S_2$ throat) by a mode sum approach, using a sharp energy cut-off and the Abel-Plana formula; Lorentz invariance is then restored by use of a Pauli-Villars regulator. The massless conformally-coupled case is found to have a logarithmic divergence (which we renormalise) and a…
Thermal Casimir Effect in A Schwarzschild-like Wormhole Spacetime
Sepuluh Nopember Institute of Technology（十十一月理工大学）；Universitas Islam Negeri Maulana Malik Ibrahim Malang（穆拉纳马利克伊布拉欣伊斯兰国立大学）；Asia Pacific Center for Theoretical Physics（亚太理论物理中心）；National Research and Innovation Agency (BRIN)（国家研究与创新署）；Universitas Indonesia（印度尼西亚大学）
In this paper, we investigate the role of gravito-inertial effects on the Casimir energy of a massless scalar field confined between two parallel plates orbiting a static and zero tidal Schwarzschild-like wormhole, at zero temperature. Firstly, we obtain the metric in isotropic coordinates, finding the allowed angular velocities and the circular orbit radii for a material particle as well as for the photon. Following, we compute the changes induced by both gravity and rotation of the plates in the energy density of the quantum vacuum fluctuations associated to the scalar field, in the zero tid…
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 (2019) 79: 951]. In particular, we consider three types of the 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 GUP principle. To this end, we consider three specific models of the redshift function along with two different EoS of state given by $\mathcal{P}_r(r)=ω_r(r) ρ(r)$ along with $\mathcal{P}_t(r)=ω_t (r)\…
Wormholes (WH) require negative energy, and therefore an exotic matter source. Since Casimir energy is negative, it has been speculated as a good candidate to source that objects a long time ago. However only very recently a full solution for $D = 4$ has been found by Garattini, thus the Casimir energy can be a source of traversable WHs. In the manuscript published by the authors, we show that this solution is possible for all space-time of dimension $D > 3$. Recently, Garattini sought to analyze the effects of Yukawa-type terms on shape functions and obtained promising results. However, it as…
In this work, we implement the semi-analytical WKB method to explore the behaviour of a scalar field on a traversable wormhole space--time with a Casimir--like complexity reported in Eur. Phys. J. C 82, 420 (2022). We estimate the error in the computation of the quasi--normal frequencies of the scalar field at each order in the WKB and show that the order with the best accuracy is not unique. We compute the value of the quasinormal frequencies for the smallest estimated error. As an aside, we find that the imaginary part of the quasinormal modes frequencies approach to zero for the fundamental…
The evaluation of Casimir energies in curved background spacetimes is an essential ingredient to study the stability of traversable wormholes. In practice one has to calculate the contribution of the transverse-traceless component of the metric perturbation on a curved spacetime background. This implies the study of an eigenvalue equation involving a modified form of the Lichnerowicz operator. For arbitrary background spacetimes, however, such an operator does not display transverse-traceless properties, a fact that impedes the determination of the eigenvalues. Against this background, we show…
A model of space-time foam, made by $N$ wormholes is considered. The Casimir energy leading to such a model is computed by means of the phase shift method which is in agreement with the variational approach used in Refs.[9-14]. The collection of Schwarzschild and Reissner-Nordström wormholes are separately considered to represent the foam. The Casimir energy shows that the Reissner-Nordström wormholes cannot be used to represent the foam.
In this work we propose the modelling of static wormholes within the $f(R,T)$ extended theory of gravity perspective. We present some models of wormholes, which are constructed from different hypothesis for their matter content, i.e., different relations for their pressure components (radial and lateral) and different equations of state. The solutions obtained for the shape function of the wormholes obey the necessary metric conditions. They show a behaviour similar to those found in previous references about wormholes, which also happens to our solutions for the energy density of such objects…
Dynamical Stability and Quasinormal Modes of Casimir Wormholes in dRGT Massive Gravity
Government General Degree College Singur（辛格尔政府普通学位学院）；Madhabdev University（马哈德夫大学）；Khazar University（哈萨尔大学）；University of KwaZulu-Natal（夸祖鲁-纳塔尔大学）；Jadara University（贾达拉大学）
Traversable Hyperbolic Wormholes with a Casimir-Memory Source: Complexity and Shell-Free Matching
Universidade Estadual do Ceará (UECE)（塞阿拉州立大学）；Emory University（埃默里大学）；Instituto Federal de Educação Ciências e Tecnologia do Ceará (IFCE)（塞阿拉联邦教育、科学和技术学院）
Morris \& Thorne \cite{morris1} proposed geometrical objects called traversable wormholes that act as bridges in connecting two spacetimes or two different points of the same spacetime. The geometrical properties of these wormholes depend upon the choice of the shape function. In literature, these are studied in modified gravities for different types of shape functions. In this paper, the traversable wormholes having shape function $b(r)=\frac{r_0\tanh(r)}{\tanh(r_0)}$ are explored in $f(R)$ gravity with $f(R)=R+αR^m-βR^{-n}$, where $α$, $β$, $m$ and $n$ are real constants. For different value…
We propose, as a novelty in the literature, the modelling of wormholes within the particular case of the $f(R,T)$ gravity, namely $f(R,T)=R+αR^{2}+λT$, with $R$ and $T$ being the Ricci scalar and trace of the energy-momentum tensor, respectively, while $α$ and $λ$ are constants. Although such a functional form application can be found in the literature, those concern to compact astrophysical objects, such that no wormhole analysis has been done so far. The quadratic geometric and linear material corrections of this theory make the matter content of the wormhole to remarkably be able to obey th…
Wormholes are tunnels connecting different regions in space-time. They were obtained originally as a solution for Einstein's General Relativity theory and according to this theory they need to be filled by an exotic kind of anisotropic matter. In the present sense, by "exotic matter" we mean matter that does not satisfy the energy conditions. In this article we propose the modelling of wormholes within an alternative gravity theory that proposes an extra material (rather than geometrical) term in its gravitational action. Our solutions are obtained from well-known particular cases of the wormh…
