Narrow Results

In the present paper, the modeling of traversable wormholes, proposed by Morris and Thorne [Am. J. Phys.56, 395 (1988)], is performed within the $f(R)$ gravity with particular viable case $f(R)=R-\mu R_c{(\frac{R}{R_c})}^p$, where $\mu$, $R_c>0$ and $0<p<1$. The energy conditions are analyzed using the shape function $b(r)=\frac{rlog(r+1)}{log(r_0+1)}$ defined by Godani and Samanta [Int. J. Mod. Phys. D28, 1950039 (2018)] and the geometric nature of wormholes is analyzed.

Morris and Thorne [M. S. Morris and K. S. Thorne, Am. J. Phys.56, 395 (1988)] proposed geometrical objects called traversable wormholes that act as bridges in connecting two spacetimes or two different points of the same spacetime. The geometrical properties of these wormholes depend upon the choice of the shape function. In the literature, these are studied in modified gravities for different types of shape functions. In this paper, the traversable wormholes having shape function $b(r)=\frac{r_{0}tanh(r)}{tanh(r_0)}$ are explored in $f(R)$ gravity with $f(R)=R+\alpha R^m-\beta R^{-n}$, where $\alpha$, $\beta$, $m$ and $n$ are real constants. For different values of constants in function $f(R)$, the analysis is done in various cases. In each case, the energy conditions, equation of state parameter and anisotropic parameter are determined.

Morris and Thorne¹ proposed traversable wormholes, hypothetical connecting tools, using the concept of Einstein’s general theory of relativity. In this paper, the modification of general relativity (in particular $f(R,T)$ theory of gravity defined by Harko et al.²) is considered, to study the traversable wormhole solutions. The function $f(R,T)$ is considered as $f(R,T)=R+\alpha R^2+\beta T$, where $\alpha$ and $\beta$ are controlling parameters. The shape and redshift functions appearing in the metric of wormhole structure have significant contribution in the development of wormhole solutions. We have considered both variable and constant redshift functions with a logarithmic shape function. The energy conditions are examined, geometric configuration is analyzed and the radius of the throat is determined in order to have wormhole solutions in absence of exotic matter.

In this paper, the strong gravitational lensing is explored for traversable wormholes in $f(R,T)$ theory of gravity with minimally-coupled massless scalar field. First, the effective wormhole solutions are obtained using the model $f(R,T)=R+2\lambda T$, where $\lambda$ is constant, $R$ is scalar curvature and $T$ is the trace of stress-energy tensor. Furthermore, three different shape functions namely, $b(r)=\frac{r_0}{exp(r-r_0)}$ (Ref. 36), $b(r)=\frac{r_0(log(r+1))}{log(r_0+1)}$ (Refs. 35 and 37) and $b(r)=r_0{\left(\frac{r}{r_0}\right)}^{\gamma }$, $0<\gamma <1$ (Refs. 34, 35, 39, 73) are considered and studied their qualitative behavior for the construction of wormhole geometry respectively. Subsequently, gravitational lensing effect is implemented to detect the existence of photon spheres at or outside the throat of wormholes.

The present work looks for new spherically symmetric wormhole solutions of the Einstein field equations based on the well-known embedding class 1, i.e. Karmarkar condition. The embedding theorems have an interesting property that connects an $n$-dimensional space–time to the higher-dimensional Euclidean flat space–time. The Einstein field equations yield the wormhole solution by violating the null energy condition (NEC). Here, wormholes solutions are obtained corresponding to three different redshift functions: rational, logarithm, and inverse trigonometric functions, in embedding class 1 space–time. The obtained shape function in each case satisfies the flare-out condition after the throat radius, i.e. good enough to represents wormhole structure. In cases of WH1 and WH2, the solutions violate the NEC as well as strong energy condition (SEC), i.e. here the exotic matter content exists within the wormholes and strongly sustains wormhole structures. In the case of WH3, the solution violates NEC but satisfies SEC, so for violating the NEC wormhole preserve due to the presence of exotic matter. Moreover, WH1 and WH2 are asymptotically flat while WH3 is not asymptotically flat. So, indeed, WH3 cutoff after some radial distance $r=r_1>r_s$, the Schwarzschild radius, and match to the external vacuum solution.

In this paper, we analyze the wormhole solutions in $f(R)$ gravity. Specifically we sought for wormhole geometry solutions for the following three shape functions: (i) $b(r)=r_0+{\rho }_0{r}_0^{3}ln\left(\frac{r_0}{r}\right)$, (ii) $b(r)=r_0+\gamma r_0\left(1-\frac{r_0}{r}\right)$ and (iii) $b(r)=\alpha +\beta r$, under some legitimate physical conditions on the parameters as well as constants involved here with the shape functions. It is observed from the graphical plots that the behavior of the physical parameters are interesting and viable.

This paper addresses the following issues: (1) the possible existence of macroscopic traversable wormholes, given a noncommutative-geometry background and (2) the possibility of allowing zero tidal forces, given a known density. It is shown that whenever the energy density describes a classical wormhole, the resulting solution is incompatible with quantum-field theory. If the energy density originates from noncommutative geometry, then zero tidal forces are allowed. Also attributable to the noncommutative geometry is the violation of the null energy condition. The wormhole geometry satisfies the usual requirements, including asymptotic flatness.

Giving up Einstein's assumption, implicit in his 1916 field equations, that inertial mass, even in its appearance as energy, is equivalent to active gravitational mass and therefore is a source of gravity allows revising the field equations to a form in which a positive cosmological constant is seen to (mis)represent a uniform negative net mass density of gravitationally attractive and gravitationally repulsive matter. Field equations with both positive and negative active gravitational mass densities of both primordial and continuously created matter, incorporated along with two scalar fields to 'relax the constraints' on the spacetime geometry, yield cosmological solutions that exhibit inflation, deceleration, coasting, acceleration, and a 'big bounce' instead of a 'big bang,' and provide good fits to a Hubble diagram of Type Ia supernovae data. The repulsive matter is identified as the back sides of the 'drainholes' introduced by the author in 1973 as solutions of those same field equations. Drainholes (prototypical examples of 'traversable wormholes') are topological tunnels in space which gravitationally attract on their front, entrance sides, and repel more strongly on their back, exit sides. The front sides serve both as the gravitating cores of the visible, baryonic particles of primordial matter and as the continuously created, invisible particles of the 'dark matter' needed to hold together the large-scale structures seen in the universe; the back sides serve as the misnamed 'dark energy' driving the current acceleration of the expansion of the universe. Formation of cosmic voids, walls, filaments and nodes is attributed to expulsion of drainhole entrances from regions populated by drainhole exits and accumulation of the entrances on boundaries separating those regions.

We have proposed a novel shape function on which the metric that models traversable wormholes is dependent. Using this shape function, the energy conditions, equation-of-state and anisotropy parameter are analyzed in $f(R)$ gravity, $f(R,T)$ gravity and general relativity. Furthermore, the consequences obtained with respect to these theories are compared. In addition, the existence of wormhole geometries is investigated.

In this work, we explore the wormhole physics in a modified gravitational theory, called the generalized Brans–Dicke theory (GBD). In order to solve the equations in this theory, the parameterized forms for the shape function and the scalar-field function are taken. With the help of selecting a specific form of state equation, i.e. considering a relation between the transverse pressure (not the total pressure) and the energy density for matter that threads wormhole: $p_t=\alpha \rho =-\rho$, we provide some special solutions of the traversable wormhole in GBD. Given that the violation of energy conditions (ECs) of matter often induces problems on the gravitational theory, it is important to inspect the ECs of matter in modified theories. In this GBD theory, we find that the weak energy condition, the null energy condition, the dominated energy condition and the strong energy condition could be satisfied for the matter near the throat of wormhole, depending on the parameterized models and the model-parameters values. Finally, using the classical reconstruction technique in the traversable wormhole physics, we derive a Lagrangian function of gravitational field for the GBD theory.

In this paper, Noether symmetry and Killing symmetry analyses of the curved traversable wormholes of $(3+1)$-dimensional spacetime metric in a Riemannian space are discussed. Moreover, a Lie algebra analysis is shown. Using the first and second Cartan’s structure equations, we find connection forms and then the curvature 2-forms are obtained. Finally, the Ricci scalar tensor and the components of Einstein curvature are computed.

This paper investigates stability of thin-shell developed from the matching of interior traversable wormhole with exterior Ayon–Beato–Garcia–de Sitter regular black hole through cut and paste approach. We employ Israel formalism and Lanczos equations to obtain the components of surface stress-energy tensor at thin-shell. These surface stresses violate null and weak energy conditions that suggest the presence of exotic matter at thin-shell. The surface pressure explains collapse as well as expanding behavior of the developed geometry. We explore stability of the constructed thin-shell through both perturbations along shell radius as well as barotropic equation of state for three appropriate values of the shape function $b(x)=a{x}^{\alpha }+(1-a)$. It is concluded that stability of thin-shell depends on the shape function, charge and cosmological constant.

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 $f(R)$ 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.

In this paper, traversable wormholes have been studied in $f(R)=R+\alpha R^m+\beta R^{-n}$ gravity, where $\alpha$, $\beta$, $m>0$ and $n>0$ are constant. A simplest form of shape function and a logarithmic form of redshift function is considered to construct wormhole solutions. The range of parameters providing the wormhole solutions free from the matter violating the energy conditions is explored. Further, the effect of charge is analyzed on wormhole solutions.

This work is aimed at the study of traversable wormholes, proposed by Morris and Thorne [Wormholes in spacetime and their use for interstellar travel: A tool for teaching general relativity, Am. J. Phys. 56 (1988) 395], in the framework of $f(R,T)=R+\alpha R^n+\lambda T$ gravity, where $\alpha$, $\lambda$ and $n$ are constants. The wormhole solutions are obtained and analyzed by using a simplest form of shape function. Further, the existence of photon spheres outside the throat of wormhole due to the gravitational lensing effect is detected.

Horizonless compact objects with light rings are becoming more popular in recent years for numerous motives. In this paper, the conditions under which the throat of a Morris–Thorne wormhole can act as an effective photon sphere are worked out. A specific example which satisfies all the energy conditions in modified theory of gravity is considered and the formation of relativistic images is studied. We have detected photon spheres for the wormhole modeling due to the effect of strong gravitational lensing. Subsequently, we have found the expression for deflection angle in terms of the angular separation between the image and lens by determining the strong-field limit coefficients. It is found to diverge for the impact parameter corresponding to the photon sphere. We observed that the angle of Einstein ring ${𝜃}_0$ and relativistic Einstein ring ${𝜃}_{n\ge 1}$ are completely distinguishable. Given the configuration of the gravitational lensing and the radii of the Einstein ring and relativistic Einstein rings, we can distinguish between a black hole and a wormhole in principle. The stability of wormholes is examined from the positivity of the shape function and satisfaction of the flare-out condition.

This paper investigates the wormhole solutions in Rastall theory of gravity using the Karmarkar conditions. For this purpose, we choose a shape function (SF) that connects two asymptotically flat regions. We also discuss the wormhole configuration by plotting three-dimensional (3D) analysis of the embedding diagram in Euclidean space. Furthermore, we also observe the detailed graphical representation of energy conditions using the considered SF. The violation of energy conditions, especially null energy conditions (NEC), indicates the existence of exotic matter and wormholes. Hence, it can be concluded that our calculated results in the background of Rastall theory of gravity are viable and stable. The exciting feature of this work is the 3D analysis to discuss the viability of wormhole geometry

Key results from the literature pertaining to a class of nonsingular black hole mimickers are explored. The family of candidate spacetimes is for now labelled the ‘black-bounce’ family, stemming from the original so-called ‘Simpson–Visser’ spacetime in static spherical symmetry. All model geometries are analysed through the lens of standard general relativity, are globally free from curvature singularities, pass all weak-field observational tests, and smoothly interpolate between regular black holes and traversable wormholes. The discourse is segregated along geometrical lines, with candidate spacetimes each belonging to one of: static spherical symmetry, spherical symmetry with dynamics, and stationary axisymmetry.