In this work, wormholes, tunnel like structures introduced by Morris \& Thorne \cite{Morris95}, are explored within the framework of $f(R)$ gravity. Using the shape function $b(r)=r_0\big(\frac{r}{r_0}\big)^γ$, where $0<γ<1$, and the equation of state $p_r=ωρ$, the $f(R)$ function is derived and the field equations are solved. Then null, weak, strong and dominated energy conditions are analyzed and spherical regions satisfying these energy conditions are determined. Furthermore, we calculated the range of the radius of the throat of the wormhole, where the energy conditions are satisfied.
This paper investigates static wormhole solutions through Noether symmetry approach in the context of energy-momentum squared gravity. This newly developed proposal resolves the singularity of big-bang and yields feasible cosmological results in the early times. We consider the particular model of this theory to establish symmetry generators and corresponding conserved quantities. For constant and variable red-shift functions, we examine the presence of viable traversable wormhole solutions for both dust as well as non-dust matter distributions and analyze the stable state of these solutions. …
In this paper, we derive some new exact solutions of static wormholes in f(T) gravity. We discuss independent cases of the pressure components including isotropic and anisotropic pressure. Lastly we consider radial pressure satisfying a barotropic equation of state. We also check the behavior of null energy condition (NEC) for each case and observe that it is violated for the anisotropic case, while it is satisfied for isotropic and barotropic cases.
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 configuratio…
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…
This study aims to investigate the viability of a viable logarithmic f(R) gravity for inflation in giving wormhole solutions. We consider a static and spherically symmetric spacetime and two different shape functions. We found that the model provides traversable wormhole solutions shown by its violation to energy conditions. Violation to null energy condition indicates the existence of traversable wormhole and the existence of exotic matter. The equation of state parameter is less than -1 which shows the presence of phantom fluid. Furthermore, the stability of wormhole is analyzed using Tolman…
Traversable wormhole solutions in General Relativity require exotic matter sources that violate the null energy condition (NEC), and such behavior maybe avoided in modified gravity. In this study, we analyze the energy conditions for static, spherically symmetric traversable Morris-Thorne wormholes in a recently proposed viable $f(R)$ gravity model. We numerically analyze solutions considering both constant and variable redshift functions, and present wormhole space-times respecting the NEC, supported by a phantom energy-like equation of state for the source. Moreover, we analyze the stability…
In this work wormholes in viable $f(R)$ gravity models are analysed. We are interested in exact solutions for stress-energy tensor components depending on different shape and redshift functions. Several solutions of gravitational equations for different $f(R)$ models are examined. Found solutions imply no need for exotic material, while this need is implied in the standard general theory of relativity. Simple expression for WEC violation near the throat is derived and analysed. High curvature regime is also discussed, as well as the question of the highest possible values of Ricci scalar for w…
The well-known problem of wormholes in general relativity (GR) is the necessity of exotic matter, violating the Weak Energy Condition (WEC), for their support. This problem looks easier if, instead of island-like configurations, one considers string-like ones, among them, cylindrically symmetric space-times with rotation. However, for cylindrical wormhole solutions a problem is the lacking asymptotic flatness, making it impossible to observe their entrances as local objects in our Universe. It was suggested to solve this problem by joining a wormhole solution to flat asymptotic regions at some…
It is shown that among the different classes of claimed static wormhole solutions of the vacuum Brans-Dicke theory only Brans Class I solution with coupling constant $ω$ less than -1.5 (excluding the point $ω=2$) gives rise to physically viable traversable wormhole geometry. Usability of this wormhole geometry for interstellar travel has been examined.
Wormholes can be described as geometrical structures in space and time that can serve as connection between distant regions of the universe. Mathematically, general wormholes can be defined both on stationary as well as on dynamic line elements. However, general relativistic and evolving Lorentzian wormholes are less studied than their static wormhole counterpart. Accordingly, in this work we shall focus on some evolving wormhole geometries. Starting from a general class of spherically symmetric line element supporting wormhole geometries, we shall use the Einstein's field equations to develop…
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.
Scalar-tensor $f(R)$ theory of gravity is considered in the framework of a simple inhomogeneous space-time model. In this we use the reconstruction technique to look for possible evolving wormhole solutions within viable $f(R)$ gravity formalism. These $f(R)$ models are then constrained so that they are consistent with existing experimental data. Energy conditions related to the matter threading the wormhole are analysed graphically and are in general found to obey the null energy conditions (NEC) in regions around the throat, while in the limit $f(R)=R,$ NEC can be violated at large in region…
We present models of wormhole under the Finslerian structure of spacetime. This is a sequel of our previous work (Eur Phys J 75:564, 2015) where we constructed a toy model for compact stars based on the Finslerian spacetime geometry. In the present investigation, a wide variety of solutions are obtained that explore wormhole geometry by considering different choices for the form function and energy density. The solutions, like the previous work, are revealed to be physically interesting and viable models for the explanation of wormholes as far as the background theory and literature are concer…
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…
Noncommutative geometry, as conceptualized by Nicolini, Smailagic, and Spallucci, may be viewed as a slight modification of Einstein's theory. The same can be said for $f(R)$ modified gravity for an appropriate choice of the function $f(R)$. Since such an $f(R)$ could be determined from the noncommutative-geometry background, these gravitational theories make very similar predictions in the discussion of (a) dark matter and (b) traversable wormholes; they can therefore be taken as equally viable models.
This paper investigates the geometry of static traversable wormhole through Noether symmetry approach in $f(R)$ gravity. We take perfect fluid distribution and formulate symmetry generators with associated conserved quantities corresponding to general form, power-law and exponential $f(R)$ models. In each case, we evaluate wormhole solutions using constant and variable red-shift functions. We analyze the behavior of shape function, viability of constructed $f(R)$ model and stability of wormhole solutions graphically. The physical existence of wormhole solutions can be examined through null/wea…
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.
The present paper is aimed at the study of traversable wormholes in $f(R)$ gravity with a viable $f(R)$ function defined as $f(R)=R-μR_c\Big(\frac{R}{R_c}\Big)^p$, where $R$ is scalar curvature, $μ$, $R_c$ and $p$ are constants with $μ, R_c>0$ and $0<p<1$ \citep{Amendola}. The metric of wormhole is dependent on shape function $b(r)$ and redshift function $ϕ(r)$ which characterize its properties, so the shape function and redshift function play an important role in wormhole modeling. In this work, the wormhole solutions are determined for (i) $ϕ(r)=\frac{1}{r}$ and (ii) $ϕ(r)=c$ (constant) with…
In this paper, we derive some new exact solutions of static wormholes in $f(R)$ gravity supported by the matter possesses Lorentizian density distribution of a particle-like gravitational source. We derive the wormhole's solutions in two possible schemes for a given Lorentzian distribution: assuming an astrophysically viable $F(R)$ function such as a power-law form and discuss several solutions corresponding to different values of the exponent (here $F =\frac{df}{dR}$). In the second scheme, we consider particular form of two shape functions and have reconstructed f(R) in both cases. We have d…
Motivated by recent proposals of possible wormhole existence in galactic halos, we analyse the cosmological evolution of wormhole solutions in modified $f(R)$ gravity. We construct a dynamical wormhole that asymptotically approaches FLRW universe, with supporting material going to the perfect isotropic fluid described by the equation of state for radiation and matter dominated universe respectively. Our analysis is based on an approximation of a small wormhole - a wormhole that can be treated as matched with the FLRW metric at some radial coordinate much smaller than the Hubble radius, so that…
In this paper, we study static spherically symmetric wormhole solutions in extended teleparallel gravity with the inclusion of noncommutative geometry under Lorentzian distribution. We obtain expressions of matter components for non-diagonal tetrad. The effective energy-momentum tensor leads to the violation of energy conditions which impose condition on the normal matter to satisfy these conditions. We explore the noncommutative wormhole solutions by assuming a viable power-law $f(T)$ and shape function models. For the first model, we discuss two cases in which one leads to teleparallel gravi…
In this manuscript, we explore the existence of wormhole solutions exhibiting spherical symmetry in a modified gravity namely $f(R,T)$ theory by involving some aspects of non-commutative geometry. For this purpose, we consider the anisotropic matter contents along with the well-known Gaussian and Lorentizian distributions of string theory. For the sake of simplicity in analytic discussions, we take a specific form of $f(R,T)$ function given by $f(R,T)=R+λT$. For both these non-commutative distributions, we get exact solutions in terms of exponential and hypergeometric functions. By taking some…
This paper discusses several new exact solutions of static wormholes in $f(R)$ gravity with a noncommutative-geometry background, which replaces point-like structures by smeared objects. In the first part of the paper we assume the power-law form $f(R)=aR^n$ and discuss several solutions corresponding to different values of the exponent. The second part of the paper assumes a particular form of the shape function that also yields a viable solution. This investigation generalizes some of our previous work in $f(R)$ gravity, as well as in noncommutative geometry.
This study explores the Gaussian and the Lorentzian distributed spherically symmetric wormhole solutions in the $f(τ, T)$ gravity. The basic idea of the Gaussian and Lorentzian noncommutative geometries emerges as the physically acceptable and substantial notion in quantum physics. This idea of the noncommutative geometries with both the Gaussian and Lorentzian distributions becomes more striking when wormhole geometries in the modified theories of gravity are discussed. Here we consider a linear model within $f(τ,T)$ gravity to investigate traversable wormholes. In particular, we discuss the …
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 this paper, we consider wormhole geometries in the context of teleparallel equivalent of general relativity (TEGR) as well as $f(T)$ gravity. The TEGR is an alternative geometrical formulation of Einstein's general relativity, where modified teleparallel gravity or $f(T)$ gravity has been invoked as an alternative approach for explaining an accelerated expansion of the universe. We present the analytical solutions under the assumption of spherical symmetry and the existence of a conformal Killing vectors to proceed a more systematic approach in searching for exact wormhole solutions. More p…
Damghan University（达姆甘大学）；Mangalore Institute of Technology & Engineering（曼格洛尔理工工程学院）；Sri Siddhartha Institute of Technology（斯里西达塔理工大学）；Kuvempu University（库文普大学）；Pacif Institute of Cosmology and Selfology (PICS)（帕西夫宇宙学与自我学研究所（PICS））；Khazar University（哈萨尔大学）；Fukushima University（福岛大学）
In this work, we analyze the wormhole solutions in $f(R)$ gravity. Specifically we sought for wormhole geometry solutions for the following three shape functions: (i) $b(r)=r_{0}+ρ_{0}r_{0}^{3}\ln\left(\frac{r_{0}}{r}\right)$, (ii) $b(r)=r_{0}+γr_{0}\left(1-\dfrac{r_{0}}{r}\right)$, and (iii) $b(r)=α+βr$, under some legitimate physical conditions on the parameters as well as constants involved here with in the shape functions. It is observed from the graphical plots that the behaviour of the physical parameters are interesting and viable.
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…
We present an analysis of the classic wormhole geometries based on conformal Weyl gravity, rather than standard general relativity. The main characteristics of the resulting traversable wormholes remain the same as in the seminal study by Morris and Thorne, namely, that effective super-luminal motion is a viable consequence of the metric. Improving on previous work on the subject, we show that for particular choices of the shape and redshift functions the wormhole metric in the context of conformal gravity does not violate the main energy conditions at or near the wormhole throat. Some exotic …
It is proved that no wormholes can be formed in viable scalar-tensor models of dark energy admitting its phantom-like ($w < -1$) behaviour in cosmology, even in the presence of electric or magnetic fields, if the non-minimal coupling function $f(Φ)$ is everywhere positive and the scalar field $Φ$ itself is not a ghost. Some special static, spherically symmetric wormhole solutions may exist if $f(Φ)$ is allowed to reach zero or to become negative, so that the effective gravitational constant becomes negative in some region making the graviton a ghost. If $f$ remains non-negative, such solutions…
