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We check the flare out condition. Variation of b (r) against r. We have used r 0 = 1, ¯ h = 1 and β = 0.1.
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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) mo...
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... asymptotically flat metric can be seen also from the Fig.(1). Using the EoS P r (r) = ω(r)ρ(r), one can easily see that when Φ(r) = 0 (tideless wormholes) we obtain 8ω(r)ρ(r)πr 3 ...
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... see from Figs.(5-12), and similarly Figs.(13-15), NEC, WEC, and SEC, are not satisfied at the wormhole throat r = r 0 . ...
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... From Fig.(16), we observe that the quantity I V is negative, i.e., I V < 0. On the other hand we can also use the redshift exp(2Φ(r)) = 1 + γ 2 r 2 to obtain an expression for the amount of exotic matter. ...
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... From Fig.(16), we observe that the quantity I V is negative, i.e., I V < 0. On the other hand we can also use the redshift exp(2Φ(r)) = 1 + γ 2 r 2 to obtain an expression for the amount of exotic matter. Due to the limitation of space, we are going to skip the full expression for I V and give only the dependence of I V against r and a, given by Fig.(17). Hence it demonstrates the existence of spacetime geometries containing traversable wormholes that are supported by arbitrarily small quantities of "exotic matter". ...
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... this case, beside the first term which is related to the wormhole geometry, we find an effect of GUP parameter β in leading order terms on the deflection angle encoded in the second term, while the third term is related to the semiclassical quantum effects. We show graphically the dependence of deflection angle against the impact parameter in Fig. ...
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We have presented systematically the effect of the Generalized Uncertainty Principle (GUP) in Casimir wormholes space-time in the recently proposed modified gravity, the so-called symmetric teleparallel gravity or $f(Q)$ gravity. Here $Q$ is the non-metricity scalar that drives the gravitation interaction. We consider two famous GUP relations, such...
We consider the process of catastrophic expansion of a spacelike wormhole after a violation of its equilibrium state. The dynamics of deformation of the comoving reference frame is investigated. We show that the deformation has a very specific anisotropic feature. The statement made earlier by other authors, that in the process of expanding the wor...
We constructed thin-shell wormholes using the well-known “cut and paste” technique for static black holes sourced by an anisotropic fluid within the context of the Rastall gravity. Using the generalized Lanczos equations we explored the energy conditions at the wormhole’s throat along with the traversability condition. We determined the stability r...
Wormhole configurations in Einstein's general theory of relativity (GR) requires exotic matters sources violating the weak energy condition (WEC). Rastall's theory is a generalization of GR in its matter source considering a nonconserved energy-momentum (EM) tensor. Hence, on one hand, the nature of this generalization of the matter source of field...
We consider the classical Hamiltonian of the interior of the Schwarzschild black hole in Ashtekar-Barbero connection formalism. Then, inspired by generalized uncertainty principle models, we deform the classical canonical algebra and derive the effective dynamics of the model under this modification. We show that such a deformation leads to the res...
Citations
... However, only very recently a traversable wormhole solution with Casimir energy as its supporting matter has been found by Garattini [34]. After this innovative work, many researchers have investigated wormhole configurations endowed with Casimir energy in different frameworks, such as, corrections due to generalized uncertainty principle [35], modified gravity theories [36], Casimir source modified by a Yukawa term [37], Casimir wormholes in Yang-Mills theory [38] and other works [39]. ...
In recent years there has been a growing interest in the field of wormhole physics in the presence of Casimir effect. As this effect provides negative energy density, it can be utilized as an ideal candidate for the exotic matter required for creating a traversable wormhole. In the context of modified theories of gravity such as Brans–Dicke (BD) theory (Brans and Dicke 1961 Phys. Rev. 124 925), wormhole geometries have been vastly investigated. However, the scientific literature is silent on the issue of BD wormholes in the presence of Casimir energy. Our aim in the present study is to seek for static spherically symmetric solutions representing wormhole configurations in BD theory with Casimir energy as the supporting matter. The Casimir setup we assume comprises two electrically neutral, infinitely large parallel planes placed in a vacuum. We then consider the Casimir vacuum energy density of a scalar field in such a configuration with Dirichlet and mixed boundary conditions. In the former case the corresponding Casimir force is attractive and in the latter this force is repulsive. We present exact zero tidal force wormhole solutions as well as those with non vanishing redshift function for both types of Casimir energies. The conditions on wormhole solutions along with the weak (WEC) and null (NEC) energy conditions put constraints on the values of BD coupling parameter. These constraints are also subject to the value of BD scalar field at the throat and the throat radius. We therefore find that BD wormholes in the presence of Casimir energy can exist without violating NEC and WEC (for the repulsive Casimir force). Finally, we examine the equilibrium condition for stability of the obtained solutions using Tolman–Oppenheimer–Volkoff equation.
... By choosing an appropriate WH geometry, we discovered that reducing the amount of exotic matter that violates the averaged null energy condition (ANEC) is possible. For further details, one can also go with these references [65,66]. ...
In this work, we have explored wormhole solutions in F (R ,Lm) gravity by assuming Morris-Thorne
wormhole metric and F (R ,Lm) = R
2 + (1 + γR )Lm where γ is free model parameter. We
determined the wormhole solutions by utilizing two newly developed shape functions (SF) that
satisfy all basic conditions for a wormhole’s physical validity. We also observe that the null
energy condition (NEC) behaves negatively. Finally, for both models, we use the volume integral
quantifier (V IQ ) and Tolman-Oppenheimer-Volkoff (TOV) equation to determine how much exotic
matter is needed near the wormhole throat and the stability of the wormhole. The extensive
detailed discussions of the matter components have been done via graphical analysis. The obtained
wormhole (WH) geometries meet the physically acceptable conditions for a stable wormhole..
... Advancements in quantum mechanics have recently centred on the notion of a minimum length, often at the Planck scale, to limit the precision of small space-time intervals and introduce positional uncertainty (MU). By redefining Casimir energy density using the generalized uncertainty principle (GUP), researchers are delving into the intriguing realm of GUP-corrected wormholes, particularly in the context of traversable wormholes [73]. Zubair and Farooq [74] explored Casimir effects with the Generalized Uncertainty Principle (GUP) on wormhole geometry in Einstein-Gauss-Bonnet gravity. ...
... It is worth mentioning that, although in our case, the null and weak conditions are satisfied near the throat of the wormhole, this is not a requirement for the formation of wormhole solutions. See for example references [75,76], where these conditions are violated. Let us now analyze if there is some region in which the conditions are violated. ...
... It is worth mentioning that, just as the null and weak energy conditions can be violated near the throat in some wormhole solutions, the strong energy conditions can also be violated. See for example references [75,76], where the strong energy condition near the throat is violated. ...
We consider the impact of Generalized Uncertainty Principle (GUP) effects on the Dymnikova regular black hole. The minimum length scale introduced by the GUP modifies the energy density associated with the gravitational source, referred to as the Dymnikova vacuum, based on its analogy with the gravitational counterpart of the Schwinger effect. We present an approximated analytical solution (together with exact numerical results for comparison) that encompasses a wide range of black hole sizes, whose properties crucially depend on the ratio between the de Sitter core radius and the GUP scale. The emergence of a wormhole inside the de Sitter core in the innermost region of the object is one of the most relevant features of this family of solutions. Our findings demonstrate that these solutions remain singularity free, confirming the robustness of the Dymnikova regular black hole under GUP corrections. Regarding energy conditions, we find that the violation of the strong, weak, and null energy conditions which is characteristic of the pure Dymnikova case does not occur at Planckian scales in the GUP corrected solution. This contrast suggests a departure from conventional expectations and highlights the influence of quantum corrections and the GUP in modifying the energy conditions near the Planck scale.
... Although there are several investigations addressing instabilities to the Ellis wormhole [7][8][9][10][11], there exists on the other hand an exotic matter source that could properly support such a geometry in general relativity (GR) [12]. Furthermore, if the modified theories of gravity are taken into account, the ghost-like scalar fields are no longer needed [13][14][15][16][17][18][19][20][21][22], which makes this traversable wormhole a viable subject for theoretical and observational physics. ...
... Moreover, we have considered that h is the Planck's constant, κ B is the Boltzmann constant, β = 1/κ B T, k is the generalized momenta, q is the generalized coordinates, H(k, q) is the Hamiltonian of the system, and N is the number of particles. Nevertheless, we see that equation (16) does not address the respective spin of particles under consideration. To step towards, such a feature must be introduced as follows ...
In this work, we analyze the thermodynamic properties of non--interacting particles under influence of the gravitational field of a traversable wormhole. In particular, we investigate how the thermodynamic quantities are affected by the Ellis wormhole geometry, considering three different regions to our study: asymptotically far, close to the throat, and at the throat. The thermodynamic quantities turn out to depend strongly on parameter that controls the wormhole throat radius. By varying it, there exist an expressive modification in the thermodynamic state quantities, exhibiting both usual matter and dark energy--like behaviors. Finally, the interactions are regarded to the energy density and it seem to indicate that it ``cures" the dark energy--like features.
... One can also go with these Refs. [65,66]. ...
... [1252,1253] (see also Refs. [1254][1255][1256]), and modifies Heisenberg's position-momentum commutator as follows: ...
Horizon-scale images of black holes (BHs) and their shadows have opened an unprecedented window onto tests of gravity and fundamental physics in the strong-field regime. We consider a wide range of well-motivated deviations from classical General Relativity (GR) BH solutions, and constrain them using the Event Horizon Telescope (EHT) observations of Sagittarius A* (Sgr A*), connecting the size of the bright ring of emission to that of the underlying BH shadow and exploiting high-precision measurements of Sgr A*’s mass-to-distance ratio. The scenarios we consider, and whose fundamental parameters we constrain, include various regular BHs, string-inspired space-times, violations of the no-hair theorem driven by additional fields, alternative theories of gravity, novel fundamental physics frameworks, and BH mimickers including well-motivated wormhole and naked singularity space-times. We demonstrate that the EHT image of Sgr A* places particularly stringent constraints on models predicting a shadow size larger than that of a Schwarzschild BH of a given mass, with the resulting limits in some cases surpassing cosmological ones. Our results are among the first tests of fundamental physics from the shadow of Sgr A* and, while the latter appears to be in excellent agreement with the predictions of GR, we have shown that a number of well-motivated alternative scenarios, including BH mimickers, are far from being ruled out at present.
... Wormholes supported by Casimir energy are treated in a variety of context in the literature. 6,22 The wormhole constructed for n = 5 falls exactly into the category of a Casimir wormhole with the constraint −2 < a5r 2 0 ≤ 0. This can be verified from Fig. 2 where ωr = p r ρ , which is nearly 3 around the throat evaluated at r 0 = 3. The wormhole constructed for n = 4 is a Casimir like wormhole with ωr positive for all values of r. Figure 2 gives a graphical representation for ωr and ωt = p t ρ in the wormhole examples for n = 4 and n = 5. ...
... The non-zero complexity factor parameterized wormholes so obtained could be classified as the Casimir wormholes. 6,21,22 The choice of the logarithmic tidal function and polynomial complexity factor makes them Casimir like wormholes with positive equation of state ωr corresponding to the radial pressure density. It may be noted that for n = 5, we could obtain a Casimir wormhole and the supporting matter in the neighborhood of the throat having ωr ≃ 3. ...
It is known that static traversable wormholes in Einstein gravity are supported by matter that violates null energy conditions (NEC). Essentially, such wormholes will be characterized by a central throat with anisotropic matter lining the throat that violates NEC. This, in turn, provides viable geometry for the wormhole to sustain. In 2018, Herrera [Phys. Rev. D 97, 044010 (2018)] introduced a new classification for spherically symmetric bodies called “complexity factor.” It was proposed that a spherically symmetric non-trivial geometry can be classified as complex or non-complex based on the nature of the inhomogeneity and anisotropy of the stress–energy tensors with only homogeneous and isotropic matter distribution leading to null complexity. Mathematically, there was also another way of obtaining zero complexity geometry. In this context, since static traversable wormholes, by default, are characterized by anisotropic and inhomogeneous matter stress tensors, the question we answer is whether it is possible to obtain zero complexity class of wormholes supported by exotic matter.
... An example of a source of exotic matter that can sustain a traversable wormhole is the Casimir vacuum energy. Thus, wormholes with Casimir-type energy density profiles have been studied in the last years [21][22][23][24][25]. In particular, [23] considered models which introduce a fundamental minimal length via Generalized Uncertainty Principle (GUP) in order to correct that energy and study wormholes solutions in the GR context. ...
... Thus, wormholes with Casimir-type energy density profiles have been studied in the last years [21][22][23][24][25]. In particular, [23] considered models which introduce a fundamental minimal length via Generalized Uncertainty Principle (GUP) in order to correct that energy and study wormholes solutions in the GR context. ...
... In sequence, we specialized the previous study for 4d wormholes, which we have called Dymnikova-Schwinger since the material source under consideration is the gravitational analogue of the pair density produced in a vacuum by means of the application of an intense (electric) field -the so-called Schwinger effect, predicted by QED. The gravitational counterpart of this phenomenon holds some similarity with that one associated to the Casimir effect, which has been widely studied in the context of wormholes [21][22][23][24][25]. Thus, on considering the correction to the Schwinger effect due to the introduction of a minimal length ( = √ α) ...
In this paper, we obtain new d -dimensional and asymptotically flat wormhole solutions by assuming a specific form of the energy density distribution. This is addressed by considering the generalization of the so-called Dymnikova model, originally studied in the context of regular black holes. In this way, we find constraints for the involved parameters, namely, the throat radius, the scale associated to the matter distribution, and the spacetime dimension, to build those wormholes. Following, we study the properties of the obtained solutions, namely, embedding diagrams as well as Weak and Null Energy Conditions (WEC and NEC). We show that the larger the dimension, the larger the flatness of the wormhole and the more pronounced the violation of these energy conditions. We also show that the corresponding fluid behaves as phantom-like for d ≥ 4 in the neighborhood of the wormhole throat. In addition, we specialize the employed model for d = 4 spacetime, associating it with the gravitational analog of the Schwinger effect in a vacuum and correcting the model by introducing a minimal length via Generalized Uncertainty Principle (GUP). Thus, we obtain a novel traversable and asymptotically flat wormhole solution by considering that the minimal length is very tiny. The associated embedding diagram shows us that the presence of this fundamental quantity increases the slope of the wormhole towards its throat compared with the case without it. That correction also attenuates the WEC (and NEC) violations nearby the throat, with the fluid ceasing to be a phantom-type at the Planck scale, unlike the case without the minimal length.
... Although there are several investigations addressing instabilities to the Ellis wormhole [7][8][9][10][11], there exists on the other hand an exotic matter source that could properly support such a geometry in general relativity (GR) [12]. Furthermore, if the modified theories of gravity are taken into account, the ghost-like scalar fields are no longer needed [13][14][15][16][17][18][19][20][21][22], which makes this traversable wormhole a viable subject for theoretical and observational physics. ...
In this work, we analyze the thermodynamic properties of non--interacting particles under influence of the gravitational field of a traversable wormhole. In particular, we investigate how the thermodynamic quantities are affected by the Ellis wormhole geometry, considering three different regions to our study: asymptotically far, close to the throat, and at the throat. The thermodynamic quantities turn out to depend strongly on parameter that controls the wormhole throat radius. By varying it, there exist an expressive modification in the thermodynamic state quantities, exhibiting both usual matter and dark energy--like behaviors.
