Wormhole Shape Research Articles

Exploring wormhole solutions with global monopole charge in the context of f(Q) gravity

This study explores the potential existence of traversable wormholes influenced by a global monopole charge within the f(Q) gravity framework. To elucidate the characteristics of these wormholes, we conducted a comprehensive analysis of wormhole solutions employing three different forms of redshift function under a linear f(Q) model. Wormhole shape functions were derived for barotropic, anisotropic, and isotropic Equations of State (EoS) cases. However, in the isotropic EoS case, the calculated shape function failed to satisfy the asymptotic flatness condition. Additionally, we observed that our obtained shape functions adhered to the flaring-out conditions under an asymptotic background for the remaining EoS cases. Furthermore, we examined the energy conditions at the wormhole throat with a radius r0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r_0$$\\end{document}. We noted the influences of the global monopole’s parameter η\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\eta $$\\end{document}, the EoS parameter ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega $$\\end{document}, and n in violating energy conditions, particularly the null energy conditions. Finally, we conducted a stability analysis utilizing the Tolman–Oppenheimer–Volkov (TOV) equation and found that our obtained wormhole solution is stable.

New Wormhole Shape Function and Energy Density Function in f(R,Lm) Gravity Theory

New Wormhole Shape Function and Energy Density Function in f(R,Lm) Gravity Theory

Fate of charged wormhole structures utilizing Karmarkar approach

The purpose of this study is to elaborate on the Morris–Thorne wormhole notion by creating a detailed model of a charged wormhole shape function. The classical embedding theory, which has played a significant role in the general theory of relativity, accomplishes this objective. Here, we assume redshift function along with charge i.e. ψ(r,Q2)=Log[1+Q2r2] and Q(r)=ξr. For this particular choice, the surface redshift function remains positive and finite everywhere even for the larger range of radial coordinate r. In wormhole geometry, the violation of Null energy condition have a crucial role which leads to the exotic matter. We examined our solutions through energy bounds (Null, Weak and Strong energy bounds) to check their stable state and its viability. Interestingly, in present work we analyze that the presence of electric charge amplify the results and provides the traversable charged wormhole solutions without exotic matter near the throat in the context of general theory of relativity.

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.

Possible existence of traversable wormhole in Finsler–Randers geometry

In the present article, we have explored the possible existence of a traversable wormhole in the framework of Finsler–Randers (F–R) geometry. In order to achieve this goal, first, we have constructed gravitational field equations for static, spherically symmetric spacetime with anisotropic fluid distribution in F–R geometry. Next, we have written the deduced form of field equations in the background of Morris–Thorne wormhole geometry. To visualize the shape of the wormhole, we have selected exponential shape function b(r)=frac{r}{expleft( eta left( frac{r}{r_{0}} - 1right) right) } with the constant parameter eta and the throat radius r_{0} and depicted two-dimensional and three-dimensional embedding diagrams corresponding to some considered values of eta and r_{0}. Moreover, all essential requirements to build a wormhole shape have been examined for the reported shape function. Next, We have analyzed wormhole configuration for three cases (I, II, III) corresponding to three selected redshift functions. Furthermore, each case is analyzed by dividing it into two models such as (i) Model-1 (for general anisotropic EoS p_{t}=chi p_{r}) and (ii) Model-2 (for linear phantom-like EoS p_{r} + omega rho =0). In each model of three cases, we have verified the validity of the wormhole solution in F–R geometry by considering null, weak, strong and dominant energy conditions. Also, the total amount of averaged NEC-violating matter near the wormhole throat has been analyzed by computing volume integral quantifier.

Yang-Mills Casimir wormholes in D = 2 + 1

This work presents new three-dimensional traversable wormhole solutions sourced by the Casimir density and pressures related to the quantum vacuum fluctuations in Yang-Mills (Y-M) theory. We begin by analyzing the noninteracting Y-M Casimir wormholes, initially considering an arbitrary state parameter ω and determine a simple constant wormhole shape function. Next, we introduce a new methodology for deforming the state parameter to find well-behaved redshift functions. The wormhole can be interpreted as a legitimate Casimir wormhole with an expected average state parameter of ω = 2. Then, we investigate the wormhole curvature properties, energy conditions, and stability. Furthermore, we discover a novel family of traversable wormhole solutions sourced by the quantum vacuum fluctuations of interacting Yang-Mills fields with a more complex shape function. Deforming the effective state parameter similarly, we obtain well-behaved redshift functions and traversable wormhole solutions. Finally, we examine the energy conditions and stability of solutions in the interacting scenario and compare to the noninteracting case.

Traversable Lorentzian wormhole on the Shtanov-Sahni braneworld with matter obeying the energy conditions

In this paper we have explored the possibility of constructing a traversable wormhole on the Shtanov-Sahni braneworld with a timelike extra dimension. We find that the Weyl curvature singularity at the throat of the wormhole can be removed with physical matter satisfying the NEC ρ + p ≥ 0, even in the absence of any effective Λ-term or any type of charge source on the brane. (The NEC is however violated by the effective matter description on the brane arising due to effects of higher dimensional gravity.) Besides satisfying NEC the matter constituting the wormhole also satisfies the Strong Energy Condition (SEC), ρ + 3p ≥ 0, leading to the interesting possibility that normal matter on the brane may be harnessed into a wormhole. Incidentally, these conditions also need to be satisfied to realize a non-singular bounce and cyclic cosmology on the brane [1] where both past and future singularities can be averted. Thus, such a cyclic universe on the brane, constituted of normal matter can naturally contain wormholes. The wormhole shape function on the brane with a time-like extra dimension represents the tubular structure of the wormhole spreading out at large radial distances much better than in wormholes constructed in a braneworld with a spacelike extra dimension and have considerably lower mass resulting in minimization of the amount of matter required to construct a wormhole. Wormholes in the Shtanov-Sahni (SS) braneworld also have sufficiently low tidal forces, facilitating traversability. Additionally they are found to be stable and exhibit a repulsive geometry. We are left with the intriguing possibility that both types of curvature singularity can be resolved with the SS model, which we discuss at the end of the concluding section.

Evolving embedded traversable wormholes in [formula omitted] gravity: A comparative study

The objective of this paper is to unveil the evolving traversable wormhole solutions within the perspective of modified f(R,G) gravity, where R is Ricci scalar and G is Gauss Bonnet term. In order to accomplish this, we develop a wormhole shape function using the Karmarkar condition for traversable static wormhole geometry, that links two asymptotically flat spacetime regions and meets the necessary requirements. The embedding diagram in two and three-dimensional Euclidean space is also discussed in order to demonstrate the wormhole configurations. For our current study, we choose two realistic and viable f(R,G) gravity models to discuss the wormhole geometry. For the traversable wormhole configurations the energy conditions must be satisfied at the throat. For this purpose, we check the energy conditions and observed that these conditions are satisfied near the throat of the wormhole space in modified f(R,G) gravity. Further, the intriguing part of this research is to perform a comparative analysis of the evolving wormhole geometries of our considered models with the help of three-dimensional graphical representation along with their regions. Moreover, we also describe the stability of obtained wormholes solutions by employing the equilibrium condition. It can be observed that our shape function acquired through the Karmarkar technique yields validated wormhole configurations with even less exotic matter correlating to the proper choice of f(R,G) gravity models. As a nutshell, we can infer that our findings fulfill all of the criterion for the presence of traversable wormhole, ensuring that our study is viable and consistent.

Heat Transfer Included Simulation of Carbonate Rock Acidizing Using Two-Scale Continuum Model with Varying Rock Physics Curves

Summary Matrix acidizing is the commonly used method to enhance permeability of a damaged zone around the well. Acid injection will dissolve the rock, creating narrow, high-permeability channels, called wormholes, to bypass the damaged zone. The pattern of wormhole generation indicates the efficiency of the well stimulation process. Although the injection rate has the most important role in this process, there are other factors such as rock properties, presence of an immiscible phase, and temperature variation that could also affect the dissolution pattern. A few studies have considered the simultaneous effects of all phenomena involved in the acidizing process. We have developed a two-phase heat transfer model coupled with a two-scale continuum model considering capillary and gravity forces for the first time, to simulate the wormhole dissolution pattern. It could be used to analyze the dissolution phenomenon of carbonate rock. A new two-phase relative permeability model is implemented to take the effect of dissolution on relative permeability curves into account. The influence of acid-rock temperature difference, reaction heat, nonisothermal condition, phase saturation, formation porosity, intrinsic permeability and heterogeneity on dissolution pattern, and number of injected pore volumes (PVs) before acid breakthrough is investigated in the developed model. The simulation results show that both optimum injection rate and required PV of acid to breakthrough are strongly dependent on acid and rock temperatures. High formation temperature increases both the optimum injection rate and the optimum number of injected PVs before breakthrough. Injection of acid at lower temperatures will decrease both the optimum injection rate and the optimum number of injected PVs to break through. Simulation results show that the optimum number of injected PVs to break through is 8% higher when reaction heat is considered. Formation properties and degree of heterogeneity influence the number of required injected PVs to breakthrough. Low porosity formations with high heterogeneity correspond to the lowest number of injected PVs to breakthrough. The results indicated that formations with higher permeability will have a higher optimum number of injected PVs to break through and an optimum injection rate. Simulated results show that increasing the initial water saturation will increase the volume of acid to breakthrough. Variation in initial water saturation has a minor effect on wormhole shape, but it does not change the dissolution regime.

Investigation of traversable wormhole solutions in modified f(R) gravity with scalar potential

The objective of this manuscript is to investigate the traversable wormhole solutions in the background of the f(R, phi ) theory of gravity, where R is the Ricci scalar and phi is the scalar potential respectively. For this reason, we use the Karmarkar criterion for traversable static wormhole geometry to create a wormhole shape function. The suggested shape function creates wormhole geometry that links two asymptotically flat spacetime regions and meets the necessary requirements. The embedding diagram in three-dimensional Euclidean space is also discussed in order to demonstrate the wormhole configurations. For our current analysis, we choose the suitable values of free parameters for f(R, phi ) gravity models to discuss the wormhole geometry. It can be observed that our proposed shape function provides the wormhole solutions with less amount of exotic matter. It can be noticed that energy conditions especially null energy conditions are violated for all considered models. The violation of energy conditions indicates the existence of exotic matter and wormhole geometry. It is concluded that the shape function acquired through the Karmarkar technique yields validated wormhole configurations with even less exotic matter correlating to the chosen f(R, phi ) gravity models.

Traversable wormhole models supported by a string cloud in rainbow gravity

The traversable wormholes are fascinating as the shortcuts in space–time. This work discusses the geometry of a traversable wormhole with a string cloud as a source in rainbow gravity. The field equations are developed and solved to obtain the wormhole’s shape function, cloud’s mass density, and string tension. We have calculated the shape function and made it specific to study the dynamics for toy model. Based on the three well-known pairs of rainbow functions (mentioned by Ali and Khalil), the string cloud’s dynamical variables including mass density and string tension are graphically presented. The corresponding energy conditions are also visually depicted. It is found that the source matter (string cloud) of the traversable wormhole must be exotic. However, the positive values of the string tension led to the presence of Casimir and dark energy effects. It is found that the toy model respects the null energy condition for a single pair of rainbow functions, i.e., Rainbow Function Type II. We have concluded that in rainbow gravity theory, the traversable wormhole solutions originating from a string cloud requires the presence of exotic matter to achieve a stable structure.

Traversable wormhole solutions admitting Karmarkar condition in f(R, T) theory

In this paper, we evaluate traversable wormhole solutions through Karmarkar condition in f(R, T) theory, where T is the trace of the energy-momentum tensor and R represents the Ricci scalar. We develop a wormhole shape function for the static traversable wormhole geometry by using the embedding class-I technique. The resulting shape function is used to construct wormhole geometry that fulfills all the necessary conditions and joins the two asymptotically flat regions of the spacetime. We investigate the existence of viable traversable wormhole solutions for anisotropic matter configuration and examine the stable state of these solutions for different f(R, T) gravity models. We analyze the graphical behavior of null energy bound to examine the presence of physically viable wormhole geometry. It is found that viable and stable traversable wormhole solutions exist in this modified theory of gravity.

Tideless traversable wormholes surrounded by cloud of strings in f(R) gravity

We study the tideless traversable wormholes in the f(R) gravity metric formalism. First we consider three shape functions of wormholes and study their viabilities and structures. The connection between the f(R) gravity model and wormhole shape function has been studied and the dependency of the f(R) gravity model with the shape function is shown. We also obtain a wormhole solution in the f(R) gravity Starobinsky model surrounded by a cloud of strings. In this case, the wormhole shape function depends on both the Starobinsky model parameter and the cloud of strings parameter. The structure and height of the wormhole is highly affected by the cloud of strings parameter, while it is less sensitive to the Starobinsky model parameter. The energy conditions have been studied and we found the ranges of the null energy condition violation for all wormhole structures. The quasinormal modes from these wormhole structures for the scalar and Dirac perturbations are studied using higher order WKB approximation methods. The quasinormal modes for the toy shape functions depend highly on the model parameters. In case of the Starobinsky model's wormhole the quasinormal frequencies and the damping rate increase with an increase in the Starobinsky model parameter in scalar perturbation. Whereas in Dirac perturbation, with an increase in the Starobinsky model parameter the quasinormal frequencies decrease and the damping rate increases. The cloud of strings parameter also impacts prominently and differently the quasinormal modes from the wormhole in the Starobinsky model.

Traversable wormholes in Rastall teleparallel gravity with non-commutative geometry

The current study explores new wormhole models with the framework of Rastall teleparallel theory. For this study, we are working with non-commutative geometry with Gaussian and Lorentzian distributions. The static and spherically symmetric spacetime is taken with the anisotropic source of fluid. Further, we compare the matter density with the Gaussian and Lorentzian distributions and get two different differential equations involving shape functions. The exact solution for the wormhole shape function is calculated for both distributions. The expression for energy conditions is provided. The graphical behavior of shape functions and energy conditions is presented for Rastall teleparallel theory under the current scenario. All the inquired results with necessary findings are concluded.

Generalized Ellis-Bronnikov bilayer graphene wormholelike surface

In this paper, we investigate the spinless stationary Schr\"odinger equation for the electron when it is permanently bound to a generalized Ellis-Bronnikov bilayer graphene wormholelike surface. The curvature gives rise to a geometric potential affecting thus the electronic dynamics. The geometry of the wormhole's shape is controlled by the parameter $n$ which assumes even values. We discuss the role played by the parameter $n$ and the orbital angular momentum on bound states and probability density for the electron.

New wormhole shape functions in f(R,T) theory of gravity

In this paper, we introduce two new shape functions of wormholes in [Formula: see text] gravity. Both shape functions are satisfied by various geometric conditions. We will also discuss the different energy conditions and geometric behavior corresponding to each shape function in different states. Finally, we investigate the system’s stability with a solution corresponding to the two shape functions.

Traversable wormholes with charge and non-commutative geometry in the [formula omitted] gravity

We consider modified symmetric teleparallel gravity (STG), in which gravitational Lagrangian is given by the arbitrary function of non-metricity scalar Q to study static and spherically symmetric charged traversable wormhole solutions with non-commutative background geometry. The matter source at the wormhole throat is acknowledged to be anisotropic, and the redshift function has a constant value (thus, our wormhole solution is non-tidal). We study the obtained field equations with the two functional forms of f(Q) STG models, such as linear f(Q)=αQ+β and non-linear f(Q)=Q+mQn models under Gaussian and Lorentzian distributions. Our analysis found the exact wormhole solutions for the linear STG model only. Also, for the non-linear model, we derived numerically suitable forms of wormhole shape functions directly from the modified Einstein Field Equations (EFEs). Besides, we probed these models via Null, Dominant, and Strong energy conditions with respect to free Modified gravity (MOG) parameters α, β, m, and n. We also used Tolman–Oppenheimer–Vokloff (TOV) equation to investigate the stability of wormhole anisotropic matter in considered MOG. Finally, we plot the equation of state.

Traversable wormhole solutions in f(R) gravity via Karmarkar condition

Motivated by recent proposals of possible wormhole shape functions, we construct a wormhole shape function by employing the Karmarkar condition for static traversable wormhole geometry. The proposed shape function generates wormhole geometry that connects two asymptotically flat regions of spacetime and satisfies the required conditions. Further, we discuss the embedding diagram in three-dimensional Euclidean space to present the wormhole configurations. The main feature of current study is to consider three well-known f(R) gravity models, namely exponential gravity model, Starobinsky gravity Model and Tsujikawa f(R) gravity model. Moreover, we investigate that our proposed shape function provides the wormhole solutions with less (or may be negligible) amount of exotic matter corresponding to the appropriate choice of f(R) gravity models and suitable values of free parameters. Interestingly, the solutions obtained for this shape function generate stable static spherically symmetric wormhole structure in the context of non-existence theorem in f(R) gravity. This may lead to a better analytical representation of wormhole solutions in other modified gravities for the suggested shape function.

Morris–Thorne wormhole with Karmarkar condition

In this paper, we construct a wormhole shape function by using Karmarkar condition. We observe that our proposed shape function connects two asymptotically flat regions, which shows the existence of Morris–Thorne traversable wormhole. Moreover, we also represent the embedding diagram in three-dimensional Euclidean space which can be extended from throat to infinity. Further, the Null and Weak energy conditions are discussed in detail. With this shape function, the anisotropic factor exhibits a repulsive nature at the throat. We support all the analysis of this work through graphical representation. It is concluded that our proposed model fulfills all the necessary conditions and shows the existence of exotic matter in the formulism of wormhole geometry in the context of General Relativity.

Model of wormholes under Krori-Barua spacetime in the presence of matter

We intend to investigate particular models of wormholes with ordinary matter source. The exact wormhole solutions are deduced by numerically solving the Einstein’s field equations with the stress-energy-tensor components. A particular form of feasible wormhole shape function is utilized. We study the solutions considering the Krori-Barua (KB) ansatz [K.D. Krori and J. Barua, J. Phys. A: Math. Gen. 8, 508 (1975)] in presence of perfect fluid matter. The obtained solutions are free from central singularity. The wormhole model thus obtained under Krori-Barua spacetime satisfies the flare-out conditions. Some physical features are briefly discussed.