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Casimir wormhole solutions in [formula omitted] gravity

In this paper, we study the Casimir effect on the wormhole geometry in f(R,Lm) gravity. We derive the field equations for the generic f(R,Lm) function by assuming static and spherically symmetric Morris–Thorne wormhole metric. Then we consider two non-linear f(R,Lm) models, specifically, f(R,Lm)=R2+Lmβ and f(R,Lm)=R2+(1+αLm)Lm where α and β are free parameters. We derive the shape functions for wormholes by utilizing the Casimir effect and examining their existence. Subsequently, we analyse the obtained wormhole solutions for each scenario, assessing the energy conditions at the wormhole throat with a radius of r0. Our findings reveal that for some arbitrary quantities, there is a violation of classical energy conditions at the wormhole throat. Additionally, we delve into the behaviour of the equation of state (EoS) for each case. Furthermore, we explore the stability of the Casimir effect wormhole solutions by employing the generalized Tolman–Oppenheimer–Volkoff (TOV) equation. Finally, we utilize the volume integral quantifier to determine the amount of exotic matter required near the wormhole throat for both models.

A study of an embedding class-I traversable wormhole in Galileon Gravity

In this article, we examine the possibility of the creation of a traversable wormhole geometry in Galileon Gravity (GG). In this gravity, the alternation of gravity is determined by an effective scalar field ϕ, treated as the Galileon field. From a mechanism perspective, GG is developed by covariantizing the decoupling Lagrangian of the DGP (Dvali-Gabadadze-Porrati) model. Now, to achieve our aim, gravitational field equations have been constructed corresponding to a line element, which represents a static and spherically symmetric spacetime. Next, we have modified these field equations in the context of a Morris-Thorne traversable wormhole spacetime. In particular, we have used the ‘Karmarkar condition’ to evaluate the wormhole solutions in a general sense. Further, for a better understanding of our obtained wormhole solutions, 2-dimensional and 3-dimensional diagrams have been displayed. Later, we scrutinized the possible creation of a traversable wormhole based on the essential requirements, that is, the infraction of energy conditions in the neighborhood of the throat region, especially the Null Energy Condition (NEC). For this purpose, we have discussed three cases like Case-I: without the necessity of dark energy (DE), Case-II: with support of phantom-like DE and Case-III: with the SFDM profile of a dark matter (DM) halo. Next, we have examined the hydrostatic equilibrium position corresponding to our obtained wormhole system in GG. Furthermore, to examine the small and sufficient quantity of exotic matter, the possible formation of a traversable wormhole has been explored by a volume integral quantifier. Lastly, we have shown the nature of active mass. Finally, we have concluded that traversable wormhole solutions can also be established in the presence of an effective scalar field without any essential support of exotic matter in the neighborhood of the throat region by GG.

A study of Yukawa–Casimir wormholes in some Rastall frameworks via conformal killing vectors approach

Present work explores the possibility of obtaining analytical wormhole solutions in Rastall theory of gravity and its modified torsion based version where the conformal killing vectors are introduced. To achieve this target, we assume spherically symmetric wormhole metric with anisotropic background matter and find the analytical solutions by taking Casimir as well as Yukawa corrected energy densities into account. The formulated solutions are then examined graphically for checking the essential properties of wormhole configuration and also, the impact of Rastall parameter, in this respect, is explored. It is found that primary wormhole properties hold in all cases while the obtained wormhole solutions in torsion based Rastall theory do not fulfill asymptotic flatness criteria for some certain choices of Rastall parameter. Further, behavior of null energy constraint is explored and the volume integral quantifier is computed for each case. We also discuss the equilibrium of proposed wormhole configurations by checking the behavior of four different forces using generalized Tolman–Oppenheimer–Volkoff equation in Rastall background (as the equilibrium condition gets modified) and conclude that these forces refer to the stability of the system in all cases, especially when one moves away from the wormhole throat.

Possibility of stable thin-shell around wormholes within string cloud and quintessential field via the van der Waals and polytropic EOS

In this work, we present the Einstein field equations (EFE) in the framework of a modified matter source and thus find out the solutions for the Wormhole. To obtain characteristic solutions set, we employ two kinds of equations of states (EOS), i.e., the van der Waals and polytropic EOS to the EFE. We adopt embedding class as a general technique for the system and discuss several physical attributes of the stellar system under embedded wormhole solutions. Detailed discussion about the matter contents of the thin-shell developed around the obtained wormhole solutions in the background of Schwarzschild BH surrounded by cloud and quintessence-type fluid distribution by using a well-known cut and paste approach. We have also performed stability analysis using the linearized radial perturbation method for the van der Waals EOS and polytropic EOS. Several interesting points have evolved from the entire investigation along with the features of the thin shell around the wormhole. It is interesting to mention that the van der Walls equation of state plays a remarkable role to maintain the stability of the thin-shell around the wormhole structure as compared to polytropic model for both choices of shape functions.

Class of charged traversable Casimir wormholes in f(R,T) gravity

This article investigates the existence and viability of some traversable wormholes involving electric charge effects in f(R,T) gravity. We use the negative energy density obtained from the Casimir source in this regard, and the consequences of the electromagnetic field produced by an electric charge are taken into account. In order to obtain wormhole shape function, we apply some noteworthy Casimir energy density systems like two parallel plates, two parallel cylinders, two spheres that are placed far apart, and the generalized uncertainty principle (GUP) correction. We analyze the fundamental wormhole conditions as well as the validity of null energy condition by taking variations of coupling parameter λ of f(R,T) gravity and the electric charge Q. Next, we explore the dynamics of gravitational active mass of the formulated wormhole solutions depending on Q. Furthermore, we study the volume integral quantifier of these charged Casimir wormhole solutions and also, determine the corresponding values of complexity factor. It is shown that the obtained wormhole solutions exhibit valid behavior and the respective values of complexity factor always fall within a certain range.

Casimir Wormholes driven by non-commutative geometries in higher dimensional Einstein Gauss–Bonnet gravity

This manuscript investigates the construction of a new class of wormhole solutions motivated by non-commutative geometry in fusion with Casimir wormholes in Einstein Gauss–Bonnet (EGB) gravity . It is not likely to ensure that the violation at small scales is significant enough to produce a macroscopic wormhole by depending merely on the Casimir effect. In our strategy, we solely utilised modifications to the energy–momentum tensor (EMT) in the non-commutative background, coupled with the impact of Casimir phenomena. On the other hand, the Einstein tensor remains unchanged in the Einstein field equations. In this regard, we have assumed four cases of non-commutative effects combined with the Casimir wormholes. We have investigated the non-commutative effects using Gaussian and Lorentzian distributions. Also, we incorporated the Casimir and Generalised Uncertainty Principle (GUP) corrected Casimir wormholes to study the basic features of wormhole solutions. The dynamics of a theory that relates the Gauss–Bonnet (GB) parameters (μ) and non-commutative parameter (β) have been addressed graphically, with a particular focus on analysing null energy conditions (NEC) through contour plots to identify the presence of exotic matter. Furthermore, embedding diagrams have been used to investigate the geometry of newly produced asymptotically flat wormholes. Additionally, the active gravitational mass has been calculated and plotted up to the radius r in the area around the wormhole throat. We have discussed equilibrium conditions to analyse the stability of obtained wormhole solutions. Finally, to understand the complexity of wormhole solutions, we have examined the complexity factor graphically.

Constructing traversable wormhole solutions in [formula omitted] theory

This paper aims to explore the viable and stable geometry of traversable wormholes in the framework of f(R,Lm) theory. For this purpose, we build a shape function using the Karmarkar condition that determines the geometry of the wormhole. The resulting shape function meets all the fundamental requirements and successfully establishes a connection between two asymptotically flat regions of the spacetime. We then formulate the field equations corresponding to two different models of this theory, representing static spherically symmetric anisotropic fluid distribution. We also check feasibility of the obtained wormhole solutions by graphically analyzing the behavior of null energy conditions. Finally, we examine the stability of these solutions through the speed of sound and adiabatic index criteria. We conclude that both our resulting models are well-agreed with the requirements needed for the existence of wormholes for chosen parametric values.

Model-independent traversable wormholes from baryon acoustic oscillations

In this paper, we investigate the model-independent traversable wormholes from baryon acoustic oscillations. Firstly, we place the statistical constraints on the average dark energy equation of state ωav by only using BAO data. Subsequently, two specific wormhole solutions are obtained, i.e, the cases of the constant redshift function and a special choice for the shape function. For the first case, we analyze the traversabilities of the wormhole configuration, and for the second case, we find that one can construct theoretically a traversable wormhole with infinitesimal amounts of average null energy condition violating phantom fluid. Furthermore, we perform the stability analysis for the first case, and find that the stable equilibrium configurations may increase for increasing values of the throat radius of the wormhole in the cases of a positive and a negative surface energy density. It is worth noting that the obtained wormhole solutions are static and spherically symmetrical metric, and that we assume ωav to be a constant between different redshifts when placing constraints, hence, these wormhole solutions can be interpreted as stable and static phantom wormholes configurations at some certain redshift which lies in the range [0.32, 2.34].

Non-commutative wormhole in non-minimal curvature–matter coupling of f(R) gravity with Gaussian and Lorentzian distributions

In this work, we construct two new wormhole solutions in the theory dealing with non-minimal coupling between curvature and matter. We take into account an explicitly non-minimal coupling between an arbitrary function of scalar curvature [Formula: see text] and the Lagrangian density of matter. For this purpose, we discuss the Wormhole geometries inspired by non-minimal curvature coupling in [Formula: see text] gravity for linear model in [Formula: see text] as well as nonlinear model in [Formula: see text]. To derive these solutions, we choose the Gaussian and Lorentzian density distributions. To check the viability of these solutions, we plot the graphs for energy conditions and wormhole parameters. It is found that obtained wormhole solutions in both distributions satisfy the energy condition. The resulting wormhole solutions for both non-commutative distributions are determined to be physically stable when we evaluate the stability of these wormhole solutions graphically. It is concluded that wormhole solutions exist with viable physical properties in the non-minimal curvature–matter coupling of [Formula: see text] gravity with Gaussian and Lorentzian distributions.

Yukawa–Casimir Wormholes in f(Q) Gravity

Casimir energy is always suggested as a possible source to create a traversable wormhole. It is also used to demonstrate the existence of negative energy, which can be created in a lab. To generalize this idea, Yukawa modification of a Casimir source has been considered in Remo Garattini (Eur. Phys. J. C 81 no.9, 824, 2021). In this work, we explore the Yukawa–Casimir wormholes in symmetric teleparallel gravity. We have taken four different forms of f(Q) to obtain wormhole solutions powered by the original Casimir energy source and Yukawa modification of the Casimir energy source. In power law form f(Q)=αQ2+β and quadratic form f(Q)=αQ2+βQ+γ, where α,β,γ are constants and Q is non-metricity scalar, we analyze that wormhole throat is filled with non-exotic matter. We find self-sustained traversable wormholes in the Casimir source where null energy conditions are violated in all specific forms of f(Q), while after Yukawa modification, it is observed that violation of null energy conditions is restricted to some regions in the vicinity of the throat.

Casimir wormholes in modified symmetric teleparallel gravity

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 symmetric teleparallel gravity or f(Q) gravity, where the non-metricity scalar Q drives the gravitation interaction. We consider three systems of the Casimir effect such as (i) two parallel plates, (ii) two parallel cylindrical plates, and (iii) two-sphere separated by a large distance to make it more experimentally feasible. Further, we studied the obtained wormhole solutions for each case with energy conditions at the wormhole throat with radius r_0 and found that some arbitrary quantity violates the classical energy conditions at the wormhole throat. Furthermore, the behavior of the equation of state (EoS) is also analyzed for each case. Finally, we investigate the stability of the obtained Casimir effect wormhole solutions with the generalized Tolman–Oppenheimer–Volkoff (TOV) equation.

Static spherically symmetric wormholes in gravity* *M.T. acknowledges University Grants Commission (UGC), New Delhi, India, for awarding National Fellowship for Scheduled Caste Students (UGC-Ref. No.: 201610123801). Z.H. acknowledges the Department of Science and Technology (DST), Government of India, New Delhi, for awarding a Senior Research Fellowship (File No. DST/INSPIRE Fellowship/2019/IF190911). PKS acknowledges National Board for Higher Mathematics (NBHM) under Department

In this study, we obtain wormhole solutions in the recently proposed extension of symmetric teleparallel gravity, known as gravity. Here, the gravitational Lagrangian L is defined by an arbitrary function f of Q and T, where Q is a non-metricity scalar, and T is the trace of the energy-momentum tensor. In this study, we obtain field equations for a static spherically symmetric wormhole metric in the context of general gravity. We study the wormhole solutions using (i) a linear equation of state and (ii) an anisotropy relation. We adopt two different forms of , (a) linear and (b) non-linear , to investigate these solutions. We investigate various energy conditions to search for preservation and violation among the obtained solutions and find that the null energy condition is violated in both cases of our assumed forms of . Finally, we perform a stability analysis using the Tolman-Oppenheimer-Volkov equation.

Wormhole solutions and energy conditions in f(R; T) gravity with exponential models

In the present article, we explore the new exact solutions of wormhole geometry by imposing the nonconstant Ricci scalar under inhomogeneous spacetime in the modified f(R; T) theory of gravity. We take two dissimilar models of f1(R) that are f1(R) = R 􀀀 (1 􀀀 e 􀀀R ) known as exponential gravity model and f1(R) = R 􀀀 tanh(R ) known as Tsujikawa model, where; are model parameters. We explore the feasible solutions for these models. Moreover, we discuss analytically and graphically the different properties of these models of wormholes by giving suitable values to the model parameters. We consider a specific shape functions i.e., b(r) = r0 log( r r0 + 1) and discuss the energy conditions for the above mentioned two models. Conclusively, we find that obtained wormhole solutions are physically acceptable with the considered exponential and Tsujikawa gravity models with or without the presence of exotic matter.

Existence of wormholes in f(𝒢) gravity using symmetries

The current study examines the geometry of static wormholes with anisotropic matter distribution in the context of modified [Formula: see text] gravity. We consider the well-known Noether and conformal symmetries, which help in investigating wormholes in [Formula: see text] gravity. For this purpose, we develop symmetry generators associated with conserved quantities by taking into consideration the [Formula: see text] gravity model. Moreover, we use the conservation relationship gained from the classical Noether method and conformal Killing symmetries to develop the metric potential. These symmetries provide a strong mathematical background to investigate wormhole solutions by incorporating some suitable initial conditions. The obtained conserved quantity performs a significant role in defining the essential physical characteristics of the shape-function and energy conditions. Further, we also describe the stability of obtained wormholes solutions by employing the equilibrium condition in modified [Formula: see text] gravity. It is observed from graphical representation of obtained wormhole solutions that Noether and conformal Killing symmetries provide the results with physically accepted patterns.

Traversable wormhole inspired by non-commutative geometries in [formula omitted] gravity with conformal symmetry

This article is based on the study of wormhole geometries in the context of symmetric teleparallel gravity or f(Q) gravity, where Q is the non-metricity scalar, and it is responsible for the gravitational interaction. To discuss the wormhole solutions, we consider spherically symmetric static spacetime metric with anisotropic matter contents under well-known non-commutative distributions known as Gaussian and Lorentzian distributions with an extra condition of permitting conformal killing vectors (CKV). This work aims to obtain wormhole solutions under these distributions, and through we found that wormhole solutions exist under these Gaussian and Lorentzian sources with viable physical properties. Further, we examine the stability of our obtained solutions through Tolman–Oppenheimer–Volkoff (TOV) equation and found that our calculated results are stable.

Wormhole solutions via embedding approach in ℛ + βℛ2 gravity with matter coupling

In this paper, we examine the embedded wormhole solutions in the modified [Formula: see text] theory of gravity, where [Formula: see text] denotes the trace of the energy–momentum tensor and [Formula: see text] is the Ricci scalar. We derive the embedded class-1 solutions by considering spherically symmetric static spacetime. The shape function is calculated in the framework of embedded class-1 spacetime. It is necessary to mention here that the calculated shape function can be used in other modified theories of gravity. We explore the feasible solutions for the specific model of [Formula: see text] theory of gravity. Energy conditions have been explored using the approach mentioned above. Conclusively, we find that obtained wormhole solutions are acceptable, as the null energy condition is violated in the specific region.

Wormhole solutions in symmetric teleparallel gravity

In this letter we obtain wormhole solutions from the Karmarkar condition in f(Q) gravity formalism, in which Q is the nonmetricity scalar. We show that the combination of such ingredients provides us the possibility of obtaining traversable wormholes satisfying the energy conditions. Our results contribute to f(Q) gravity ascension, that was recently ignited by the natural prediction of early and late-time stages of universe expansion acceleration in the formalism.

Charged traversable wormholes in f(R) gravity

This work is focused on the study of charged wormholes in the following two aspects: (i) to obtain exotic matter free effective charged wormhole solutions and (ii) to determine deflection angle for gravitational lensing effect. We have defined a novel redshift function, obtained wormhole solutions using the background of [Formula: see text] theory of gravity and found the regions obeying the weak energy condition. Further, the gravitational lensing effect is analyzed by determining the deflection angle in terms of strong field limit coefficients.

Modeling of traversable wormholes in exponential f(R, T) gravity

In the present communication, we have studied the existence of wormholes described by a logarithmic shape function, in the exponential f(R, T) gravity given by f(R, T) = R + 2ξeζt where ξ and ζ are arbitrary constants, under three different sets of physical constraints. The logarithmic shape function is well behaved, satisfying all the necessary constraints for traversable and asymptotically flat wormholes. The obtained wormhole solutions are analyzed from the energy conditions for different values of involved physical constants. It has been observed that our proposed shape function for the exponential form of f(R, T) gravity represents the existence of exotic matter with a standard violation of the NEC. Moreover, for the trace T = 0, for the general relativity case with R being replaced by R + 2, the wormhole geometry has been analyzed to prove the existence of exotic matter. Further, the behaviour of physical parameters, such as the energy density ρ, the trace T, and anisotropy parameter Δ, describing the geometry of the universe has been presented with the help of graphs.

Traversable wormholes with logarithmic shape function in f(R,T) gravity

In this work, a new form of the logarithmic shape function is proposed for the linear [Formula: see text] gravity, [Formula: see text] where [Formula: see text] is an arbitrary coupling constant, in wormhole geometry. The desired logarithmic shape function accomplishes all necessary conditions for a traversable and asymptotically flat wormhole. The obtained wormhole solutions are analyzed from the energy conditions for different values of [Formula: see text]. It has been observed that our proposed shape function for the linear form of [Formula: see text] gravity, represents the existence of exotic matter and non-exotic matter. Moreover, for [Formula: see text] i.e. for the general relativity case, the existence of exotic matter for the wormhole geometry has been confirmed. Further, the behavior of the radial state parameter [Formula: see text], the tangential state parameter [Formula: see text], and the anisotropy parameter △ describing the geometry of the universe, has been presented for different values of [Formula: see text] chosen in [Formula: see text].