Non-commutativity is a key feature of spacetime geometry. The current article explores the traversable wormhole solutions in the framework of $f(R,L_m)$ gravity within non-commutative geometry. By using the Gaussian and Lorentzian distributions, we construct tideless wormholes for the nonlinear $f(R,L_m)$ model $f(R,L_m)=\dfrac{R}{2}+L_m^α$. For both cases, we derive shape functions and discuss the required different properties with satisfying behavior. For the required wormhole properties, we develop some new constraints. The influence of the involved model parameter on energy conditions is analyzed graphically which provides a discussion about the nature of exotic matter. Further, we check the physical behavior regarding the stability of wormhole solutions through the TOV equation. An interesting feature regarding the stability of the obtained solutions via the speed of sound parameters within the scope of average pressure is discussed. Finally, we conclude our results.
Traversable wormholes in General Relativity (GR) require exotic matter sources that violate the null energy condition (NEC), and such behavior may be avoided in modified gravity. Moreover, the concept of non-commutative geometry as a gravitational source can be leveraged both in GR and modified gravity to realize non-trivial space-time configurations. In this study, we use $f(R)$ gravity in conjunction with non-commutative geometry to analyze spherically symmetric traversable Morris-Thorne wormhole solutions from the aspect of energy condition violation, considering both constant and variable …
In the present work we search for a new wormhole solution inspired by noncommutative geometry with the additional condition of allowing conformal Killing vectors (CKV). A special aspect of noncommutative geometry is that it replaces point-like structures of gravitational sources with smeared objects under Gaussian distribution. However, the purpose of this paper is to obtain wormhole solutions with noncommutative geometry as a background where we consider a point-like structure of gravitational object without smearing effect. It is found through this investigation that wormhole solutions exist…
Einstein-Gauss-Bonnet gravity is a generalization of the general relativity to higher dimensions in which the first and second-order terms correspond to general relativity and Einstein-Gauss-Bonnet gravity respectively. We construct a new class of five-dimensional (5D) thin-shell wormholes by the `Cut-Paste' technique from black holes in Einstein-Gauss-Bonnet gravity inspired by non-commutative geometry starting with a static spherically symmetric, Gaussian mass distribution as a source and for this structural form of the thin shell wormhole we have explored several salient features of the sol…
A new solution has been presented for the spherically symmetric space time describing wormholes with Phantom Energy. The model suggests that the existence of wormhole is supported by arbitrarily small quantity of Phantom Energy.
Traversible wormhole space-times are found as static, spherically symmetric solutions to the Einstein equations with ingoing and outgoing pure ghost radiation, i.e. pure radiation with negative energy density. Switching off the radiation causes the wormhole to collapse to a Schwarzschild black hole.
It is generally believed that wormholes are supported by exotic matter violating Null Energy Condition (NEC). However, various studies of wormhole geometries under Lovelock theories of gravity have reported existence of wormhole supported by matter satisfying NEC. Being inspired by these results, we explore the possibility of the existence of wormhole supported by normal quark matter in third order Lovelock gravity theory. Well known MIT Bag Model Equation of state is chosen for describing the quark matter. Taking physically acceptable approximations, we solve the field equations for shape fun…
We analytically explore the effect of falling matter on a spherically symmetric wormhole supported by a spherical shell composed of exotic matter located at its throat. The falling matter is assumed to be also a thin spherical shell concentric with the shell supporting the wormhole, and its self-gravity is completely taken into account. We treat these spherical thin shells by Israel's formalism of metric junction. When the falling spherical shell goes through the wormhole, it necessarily collides with the shell supporting the wormhole. To treat this collision, we assume the interaction between…
Abstract This short paper investigates the harmonic behavior of a general-relativistic thin-shell wormhole supported by a particular type of exotic fluid. The exotic fluid obeys a never-studied-before metric-dependent equation of state. This equation of state is tailored such that the wormhole's throat undergoes a harmonic-like behavior before damping to an equilibrium radius. Eventually, the mirror-symmetric Schwarzschild thin-shell wormhole is studied in this framework as an example.
The purpose of this paper is to obtain exact solutions of the Einstein field equations describing traversable wormholes supported by phantom energy. Their relationship to exact solutions in the literature is also discussed, as well as the conditions required to determine such solutions.
When Morris and Thorne first proposed that traversable wormholes may be actual physical objects, they concentrated on the geometry by specifying the shape and redshift functions. This mathematical approach necessarily raises questins regarding the determination of the required stress-energy tensor. This paper discusses a natural way to obtain a complete wormhole solution by assuming that the wormhole (1) is supported by generalized Chaplygin gas and (2) admits conformal Killing vectors.
We study the problem of existence of static spherically symmetric wormholes supported by the kink-like configuration of a scalar field. With this aim we consider a self-consistent, real, nonlinear, nonminimally coupled scalar field $ϕ$ in general relativity with the symmetry-breaking potential $V(ϕ)$ possessing two minima. We classify all possible field configurations ruling out those of them for which wormhole solutions are impossible. Field configurations admitting wormholes are investigated numerically. Such the configurations represent a spherical domain wall localized near the wormhole th…
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.
Recent papers by Fewster and Roman have emphasized that wormholes supported by arbitrarily small amounts of exotic matter will have to be incredibly fine-tuned if they are to be traversable. This paper discusses a wormhole model that strikes a balance between two conflicting requirements, reducing the amount of exotic matter and fine-tuning the metric coefficients, ultimately resulting in an engineering challenge: one requirement can only be met at the expense of the other. The wormhole model is macroscopic and satisfies various traversability criteria.
In this article, we have found a series solution of 3D Einstein equations describing a wormhole for an inhomogeneous distribution of phantom energy. Here, we assume equation of state is linear but highly anistropic.
We have examined the possible construction of a stationary, spherically symmetric and spatially inhomogeneous wormhole spacetime supported by the phantom energy. The later is supposed to be represented by the modified Chaplygin gas equation of state. The solutions so obtained satisfy the flare out and the asymptotic flatness conditions. It is also shown that the averaged null energy condition has to be violated for the existence of the wormhole.
We explore the possibility that traversable wormholes be supported by specific equations of state responsible for the present accelerated expansion of the Universe, namely, phantom energy, the generalized Chaplygin gas, and the van der Waals quintessence equation of state.
Recently, spherically symmetric, static wormholes supported by exotic dust and a radial magnetic field have been derived and argued to be stable with respect to linear radial fluctuations. In this report we point out that these wormholes are unstable due to the formation of shell-crossing singularities when the nonlinearities of the theory are taken into account.
The purpose of this paper is to examine the possible existence or construction of traversable wormholes supported by generalized Chaplygin gas (GCG) by starting with a general line element and the Einstein tensor, together with the equation of state, thereby continuing an earlier study by the author of wormholes supported by phantom energy. Numerical techniques are used to demonstrate the existence of wormhole spacetimes that (1) meet the flare-out conditions at the throat, (2) are traversable by humanoid travelers, thanks to low tidal forces and short proper distances near the throat, and (3)…
The possible process of creation/annihilation of traversable wormholes in the model with phantom (ghost) scalar field is described. It is shown that such process can be realized only for some special choice of a potential energy, in particular, for the Sine-Gordon potential.
In this article, we study the possibility of sustaining a static and spherically symmetric traversable wormhole geometries admitting conformal motion in Einstein gravity, which presents a more systematic approach to search a relation between matter and geometry. In wormhole physics, the presence of exotic matter is a fundamental ingredient and we show that this exotic source can be dark energy type which support the existence of wormhole spacetimes. In this work we model a wormhole supported by dark energy which admits conformal motion. We also discuss the possibility of detection of wormholes…
It was pointed out by Fewster and Roman that some of the wormhole models discussed by Kuhfittig suffer from the failure to distinguish proper from coordinate distances. One of the advantages of "designer wormholes" is that models can be altered. The purpose of this note is to show that by adjusting the metric coefficients, some of these problems can be corrected. By doing so, the basic idea can be retained: wormholes containing only small amounts of exotic matter can still be traversable.
It is shown in the first part of this paper that a combined model comprising ordinary and quintessential matter can support a traversable wormhole in Einstein-Maxwell gravity. Since the solution allows zero tidal forces, the wormhole is suitable for a humanoid traveler. The second part of the paper shows that the electric field can be eliminated (Einstein gravity), but only by tolerating enormous tidal forces. Such a wormhole would still be capable of transmitting signals.
This paper discusses a new variable equation of state parameter leading to exact solutions of the Einstein field equations describing traversable wormholes. In addition to generalizing the notion of phantom energy, the equation of state generates a mathematical model that combines the generalized phantom energy and the generalized Chaplygin gas models.
We present new, asymptotically flat, static, spherically symmetric and traversable wormhole solutions in General Relativity which are supported by a family of ghost scalar fields with quartic potential. This family consists of a particular composition of the scalar field modes, in which each mode is characterized by the same value of the angular momentum number $\ell$, yet the composition yields a spherically symmetric stress-energy-momentum and metric tensor. For $\ell = 0$ our solutions reduce to wormhole configurations which had been reported previously in the literature. We discuss the eff…
We construct a static axisymmetric wormhole from the gravitational field of two Schwarzschild particles which are kept in equilibrium by strings (ropes) extending to infinity. The wormhole is obtained by matching two three-dimensional timelike surfaces surrounding each of the particles and thus spacetime becomes non-simply connected. Although the matching will not be exact in general it is possible to make the error arbitrarily small by assuming that the distance between the particles is much larger than the radius of the wormhole mouths. Whenever the masses of the two wormhole mouths are diff…
We provide a new model of higher dimensional wormholes supported by phantom energy derived from a scalar field with negative kinetic term. We have shown that the Averaged Null Energy Condition (ANEC) violating phantom energy can be reduced as desired. We have also noticed that dimension of the spacetime plays a crucial role for measuring the ANEC violating matter needed.
Recently in (Phys. Rev. D 76, 087502 (2007) and Phys. Rev. D 77, 089903(E) (2008)) a thin-shell wormhole has been introduced in 5-dimensional Einstein-Maxwell-Gauss-Bonnet (EMGB) gravity which was supported by normal matter. We wish to consider this solution and investigate its stability. Our analysis shows that for the Gauss-Bonnet (GB) parameter $α<0,$ stability regions form for a narrow band of finely-tuned mass and charge. For the case $α>0$, we iterate once more that no stable, normal matter thin-shell wormhole exists.
In the present paper, the modelling of traversale wormholes, proposed by Morris \& Thorne \cite{morris1}, is performed within the $f(R)$ gravity with particular viable case $f(R)=R-μR_c\Big(\frac{R}{R_c}\Big)^p$, where $μ, R_c>0$ and $0<p<1$. The energy conditions are analyzed using the shape function $b(r)=\frac{r\log(r+1)}{\log(r_0+1)}$ defined by Godani and Samanta \cite{godani} and geometric nature of wormholes is analyzed.
It is generally agreed that the acceleration of the Universe can best be explained by the presence of dark or phantom energy. The equation of state of the latter shows that the null energy condition is violated. Such a violation is the primary ingredient for sustaining traversable wormholes. This paper discusses wormholes supported by a more general form called polytropic phantom energy. The equation of state results in significant generalizations of the phantom-energy and, in some cases, the generalized Chaplygin-gas wormhole models, both of which continue to receive considerable attention fr…
In this article, we construct spherical thin-shell wormholes with charge in dilaton gravity. The exotic matter required for the construction is provided by a generalized Chaplygin gas. We study the stability under perturbations preserving the symmetry. We find that the increase of the coupling between the dilaton and the electromagnetic fields reduces the range of the parameters for which stable configurations are possible.
In this paper we study the possibility of sustaining an evolving wormhole via exotic matter made out of phantom energy. We show that this exotic source can support the existence of evolving wormhole spacetimes. Explicitly, a family of evolving Lorentzian wormholes conformally related to another family of zero-tidal force static wormhole geometries is found in Einstein gravity. Contrary to the standard wormhole approach, where first a convenient geometry is fixed and then the matter distribution is derived, we follow the conventional approach for finding solutions in theoretical cosmology. We d…
Wormholes are one of the most interesting topological features in spacetime, offering a rat run between two vastly separated regions of the universe. In this paper, we study the deflection angle of light by wormholes, which are supported by electric charge, magnetic charge, and scalar fields in the weak field limit approximation. To this end, we apply new geometric methods -- the Gauss-Bonnet theorem and the optical geometry -- to compute the deflection angles. We also verify our findings by using the well-known geodesics method. There exists a similarity between the charge and the quantum cor…
In this paper we study the possibility of sustaining an evolving wormhole via exotic matter made of phantom energy in the presence of a cosmological constant. We derive analytical evolving wormhole geometries by supposing that the radial tension of the phantom matter, which is negative to the radial pressure, and the pressure measured in the tangential directions have barotropic equations of state with constant state parameters. In this case the presence of a cosmological constant ensures accelerated expansion of the wormhole configurations. More specifically, for positive cosmological constan…
We extend the notion of phantom energy--which is generally accepted for homogeneously distributed matter with $w<-1$ in the universe--on inhomogeneous spherically symmetric spacetime configurations. A spherically symmetric distribution of phantom energy is shown to be able to support the existence of static wormholes. We find an exact solution describing a static spherically symmetric wormhole with phantom energy and show that a spatial distribution of the phantom energy is mainly restricted by the vicinity of the wormhole's throat. The maximal size of the spherical region, surrounding the thr…
Recent studies have shown that (a) quantum effects may be sufficient to support a wormhole throat and (b) the total amount of "exotic matter" can be made arbitrarily small. Unfortunately, using only small amounts of exotic matter may result in a wormhole that flares out too slowly to be traversable in a reasonable length of time. Combined with the Ford-Roman constraints, the wormhole may also come close to having an event horizon at the throat. This paper examines a model that overcomes these difficulties, while satisfying the usual traversability conditions. This model also confirms that the …
Thin-shell wormholes are constructed starting from the exotic branch of Wiltshire spherically symmetric solution of Einstein-Gauss-Bonnet gravity. The energy-momentum tensor of the shell is studied, and it is shown that configurations supported by matter satisfying the energy conditions exist for certain values of the parameters. Differing from the previous result associated to the normal branch of Wiltshire solution, this is achieved for small positive values of the Gauss-Bonnet parameter and for vanishing charge.
This paper presents a new wormhole solution by assuming that a homogeneously distributed fluid with equation of state $p=ωρ$ can be adapted to an anisotropic spacetime such as a wormhole and that this spacetime admits a one-parameter group of conformal motions. The pressure $p$ in the equation of state becomes the lateral pressure $p_t$ instead of the radial pressure $p_r$, as assumed in previous studies. Given that $p_t=ωρ$, $p_r$ is then determined from the Einstein field equations. A wormhole solution can be obtained only if $ω<-1$ or $0<ω<1$. Since the former case corresponds to phantom da…
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 f…
Wormholes with Ellis geometry have been successfully constructed using tachyon matter \cite{Das}. However, for such a wormhole, it is obtained that the redshift function is necessarily a constant, and also the wormhole is plagued with an imaginary tachyon potential and a constant field if the solutions are obtained in the absence of a cosmological constant term. So, a physically plausible wormhole solution is possible only in the presence of a $Λ$ term. In this paper, we try to construct a wormhole from tachyon matter with three $other$ geometries \textit{different} from the Ellis geometry and…
We examine the linear stability of static, spherically symmetric wormhole solutions of Einstein's field equations coupled to a massless ghost scalar field. These solutions are parametrized by the areal radius of their throat and the product of the masses at their asymptotically flat ends. We prove that all these solutions are unstable with respect to linear fluctuations and possess precisely one unstable, exponentially in time growing mode. The associated time scale is shown to be of the order of the wormhole throat divided by the speed of light. The nonlinear evolution is analyzed in a subseq…
The Zipoy-Voorhees-Weyl (ZVW) spacetime characterized by mass ($M$) and oblateness ($δ$) is proposed in the construction of viable thin-shell wormholes (TSWs). Departure from spherical / cylindrical symmetry yields positive total energy in spite of the fact that local energy density may take negative values. We show that oblateness of the bumpy sources / black holes can be incorporated as a new degree of freedom that may play role in the resolution of the exotic matter problem in TSWs. Small velocity perturbation reveals, however, that the resulting TSW is unstable.
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)\…
We consider a traversable wormhole solution of Einstein's gravity conformally coupled to a massless scalar field, a solution derived by Barcelo and Visser based on the JNWW spacetime. We study the geodesic motion of time-, light- and space-like particles in this spacetime. We solve the equations of motion analytically in terms of the Weierstraß\ functions and discuss all possible orbit types and their parameter dependence. Interestingly, bound orbits occur for time-like geodesics only in one of the two worlds. Moreover, under no conditions there exist time-like two world bound orbits.
In this paper, we construct generic, spherically symmetric thin-shell wormholes and check their stabilities using the unified dark sector, including dark energy and dark matter. We give a master equation, from which one can recover, as a special case, other stability solutions for generic spherically symmetric thin-shell wormholes. In this context, we consider a particular solution; namely we construct an effective thin-shell wormhole under Lorentz symmetry breaking. We explore stability analyses using different models of the modified Chaplygin gas with constraints from cosmological observatio…
We revisit the shapes of the throats of wormholes, including thin-shell wormholes (TSWs) in $2+1-$dimensions. In particular, in the case of TSWs this is done in a flat $2+1-$dimensional bulk spacetime by using the standard method of cut-and-paste. Upon departing from a pure time-dependent circular shape i.e., $r=a\left( t\right) $ for the throat, we employ a $% θ-$dependent closed loop of the form $r=R\left( t,θ\right) ,$ and in terms of $R\left( t,θ\right) $ we find the surface energy density $σ$ on the throat. For the specific convex shapes we find that the total energy which supports the wo…
We consider reflection-asymmetric thin-shell wormholes within Palatini $f(\mathcal{R})$ gravity using a matching procedure of two patches of electrovacuum space-times at a hypersurface (the shell) via suitable junction conditions. The conditions for having (linearly) stable wormholes supported by positive-energy matter sources are determined. We also identify some subsets of parameters able to locate the shell radius above the event horizon (when present) but below the photon sphere (on both sides). We illustrate with an specific example that such two photon spheres allow an observer on one of…
Wormholes allowed by the general theory of relativity that are simultaneously traversable by humanoid travelers are subject to severe constraints from quantum field theory, particularly the so-called quantum inequalities, here slightly extended. Moreover, self-collapse of such wormholes can only be prevented by the use of "exotic matter," which, being rather problematical, should be used in only minimal quantities. However, making the layer of exotic matter arbitrarily thin leads to other problems, such as the need for extreme fine-tuning. This paper discusses a class of wormhole geometries th…
We analyze the nonlinear evolution of spherically symmetric wormhole solutions coupled to a massless ghost scalar field using numerical methods. In a previous article we have shown that static wormholes with these properties are unstable with respect to linear perturbations. Here we show that depending on the initial perturbation the wormholes either expand or decay to a Schwarzschild black hole. We estimate the time scale of the expanding solutions and the ones collapsing to a black hole and show that they are consistent in the regime of small perturbations with those predicted from perturbat…
By a combination of analytical and numerical techniques, we demonstrate the existence of spherical, asymptotically flat traversable wormholes supported by exotic matter whose stress tensor relative to the orthonormal frame of Killing observers takes the form of a perfect fluid possessing anisotropic pressures and subject to linear equations of state: $τ=λρc^{2}$, $P=μρc^{2}$. We show that there exists a four parameter family of asymptotically flat spherical wormholes parametrized by the area of the throat A(0), the gradient $Λ(0)$ of the red shift factor evaluated at the throat as well as the …
We show that the presence of a nonminimal interaction between dark matter and dark energy may lead to a violation of the null energy condition and to the formation of a configuration with nontrivial topology (a wormhole). In this it is assumed that both dark matter and dark energy satisfy the null energy condition, a violation of which takes place only in the inner high-density regions of the configuration. This is achieved by assuming that, in a high-density environment, a nonminimal coupling function changes its sign in comparison with the case where dark matter and dark energy have relative…
Several traversable wormholes (T-WHs) of the Morris-Thorne type have been presented as exact solutions of Einstein-nonlinear electrodynamics gravity (GR-NLED), e.g. \cite{Arellano2009, Bronnikov2018,Bronnikov_Walia2021, Canate_Breton2018, Canate_Breton_Ortiz2020, Canate_Magos_Breton2020}. However, none of these solutions is support by a nonlinear electrodynamics model satisfying plausible conditions. In this work, we present the first traversable wormhole solution of Einstein-nonlinear electrodynamics gravity coupled to a self-interacting phantom scalar field (GR-NLED-SF) with a NLED model suc…
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 $f(Q)=Q+mQ^n$ models u…
We test the stability of various wormholes and black holes supported by a scalar field with a negative kinetic term. The general axial perturbations and the monopole type of polar perturbations are considered in the linear approximation. Two classes of objects are considered: (i) wormholes with flat asymptotic behavior at one end and AdS on the other (M-AdS wormholes) and (ii) regular black holes with asymptotically de Sitter expansion far beyond the horizon (the so-called black universes). A difficulty in such stability studies is that the effective potential for perturbations forms an infini…
