Narrow Results

The objective of this study is to examine the possible existence of traversable wormhole geometries within the context of $f(R,L_m,T)$ gravity. To meet this objective, we employ the Karmarkar condition to construct the shape function that aids in identifying the wormhole configurations. This developed function is found to satisfy the essential conditions and provides a link between two asymptotically flat spacetime regions. We then assume the Morris–Thorne line element that expresses the wormhole configuration and formulate the anisotropic gravitational equations for a particular minimal matter-spacetime coupled model of the modified theory. Afterward, we develop three solutions and determine their viability by analyzing whether they violate the null energy conditions. Different stability methods are applied to the resulting geometries to explore the acceptance of the considered modified model. We conclude that the developed wormhole structures potentially fulfill the required criteria and thus exist in this modified gravity under all choices of the matter Lagrangian density.

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.

In the present work, exact solutions to Einstein’s field equations are obtained in the presence of a scalar field in three cases. In the first case, the equation of state constituting the matter of wormhole is considered as $p_r=\omega \rho$, where $\omega$ is the equation of state parameter. In the second case, the pressures are assumed to follow the relation $p_r=k{p}_t$, where $k$ is a nonzero constant. In the third case, the form of matter energy density is assumed as $\rho =\frac{{\rho }_s{r}_s}{r{\left(\frac{r}{r_s}+1\right)}^n}$, where $n>1$, $r_s$ is the scale radius and ${\rho }_s$ is the corresponding matter density. In every case, the shape function is derived and its necessary conditions such as throat condition, flare out condition and asymptotic conditions are examined. By using these shape functions, the wormhole solutions are obtained and energy conditions are tested.

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.

Traversable wormholes, tunnel-like structures introduced by Morris and Thorne [Am. J. Phys.56 (1988) 395], have a significant role in connection of two different spacetimes or two different parts of the same spacetime. The characteristics of these wormholes depend upon the redshift and shape functions which are defined in terms of radial coordinate. In literature, several shape functions are defined and wormholes are studied in $f(R)$ gravity with respect to these shape functions [F. S. N. Lobo and M. A. Oliveira, Phys. Rev. D80 (2009) 104012; H. Saiedi and B. N. Esfahani, Mod. Phys. Lett. A26 (2011) 1211; S. Bahamonde, M. Jamil, P. Pavlovic and M. Sossich, Phys. Rev. D94 (2016) 044041]. In this paper, two shape functions (i) $b(r)=\frac{r_{0}log(r+1)}{log(r_0+1)}$ and (ii) $b(r)=r_0{(\frac{r}{r_0})}^{\gamma }$, $0<\gamma <1$, are considered. The first shape function is newly defined, however, the second one is collected from the literature [M. Cataldo, L. Liempi and P. Rodríguez, Eur. Phys. J. C77 (2017) 748]. The wormholes are investigated for each type of shape function in $f(R)$ gravity with $f(R)=R+\alpha R^m-\beta R^{-n}$, where $m$, $n$, $\alpha$ and $\beta$ are real constants. Varying the parameter $\alpha$ or $\beta$, $f(R)$ model is studied in five subcases for each type of shape function. In each case, the energy density, radial and tangential pressures, energy conditions that include null energy condition, weak energy condition, strong energy condition and dominated energy condition and anisotropic parameter are computed. The energy density is found to be positive and all energy conditions are obtained to be violated which support the existence of wormholes. Also, the equation-of-state parameter is obtained to possess values less than $-1$, that shows the presence of the phantom fluid and leads toward the expansion of the universe.

Morris and Thorne [Am. J. Phys.56 (1988) 395] developed wormhole solutions in General Relativity which requires the dissatisfaction of null energy condition at the throat. The current scenario of the universe has been explained by using the background of modified gravity and it has inspired the researchers to explore the wormhole solutions in modified versions of gravity. In this paper, the $f(R,T)$ theory of gravity proposed by Harko et al. [Phys. Rev. D84 (2011) 024020] is taken to investigate traversable wormhole solutions. These solutions have been developed in three cases. In each case, the shape function is derived, its characteristics are studied and the embedding surface is constructed. Further, in each case, the wormhole solutions are constructed and energy conditions are tested to know about the matter sustaining the wormhole geometries.

In this paper, the wormholes have been constructed in the framework of the linear $f(R,T)$ gravity model with noncommutative geometry. The wormhole solutions are obtained in the context of Gaussian and Lorentzian distributions of matter using $f(R,T)$ gravity. The energy conditions such as null, weak, strong, and dominant energy conditions are explored and the regions satisfying these conditions are examined for both forms of matter distributions. Further, the stability of wormhole solutions is studied with the help of TOV (Tolman–Oppenheimer–Volkoff) equations. It is found that the wormhole solutions are stable and free from exotic matter for the suitable choice of parameters.

Taking the Astley element for example, the conventional mapped infinite element is theoretically dissected in this paper. The study brings to light the reason why the results from the mapped infinite elements vary with the location of the mid-side points used in the geometry mapping. To remedy this deficiency, a new conjugated mapped infinite element is proposed whose shape functions exactly satisfy the multi-pole expansion in the infinite direction. Within the framework of this infinite element, shape functions for any type of wave are composed of the one in the conventional finite element for the same order multiplied by a factor that contains the information of the geometry mapping and the decay behavior of wave. In addition to the slight modification to the phase factor and the weighting factor, the present element permits a free geometry mapping, and therefore greatly expands the applicability of the mapped infinite element methods. To display the performance of the proposed element, typical examples are finally given.

In this work, the solutions of traversable wormholes are investigated inside modified $f(R)$ gravity under non-commutative geometry since matter possesses Lorentzian density distribution of a particle-like gravitation source. To find the exact wormhole solutions, two different shape functions $b(r)=r_0(\frac{a^r}{a^{r_0}})$, $0<a<1$, and $b(r)=r_0{(\frac{cosh(r_0)}{cosh(r)})}^{\mu }$, $0<\mu <1$, are considered. The first shape function was proposed by Mishra and Sharma [A new shape function for wormholes in $f(R)$ gravity and General Relativity, preprint (2020), arXiv:2003.00298v1 [physics.gen-ph]], however the second is newly defined in this paper. The behaviors of both shape functions are analyzed with the throat radius $r=r_0=1$. The equation-of-state (EoS) parameter energy conditions, and anisotropy parameter are discussed with graphical point of view.

The present work is focused on 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], using the background of modified gravity. It is performed by using the models: I. $f=R+2\beta T$, II. $f=R+\alpha R^n$ and III. $f=R+\alpha R^n+2\beta T$, where $\alpha$, $\beta$ and $n$ are constants. The Model I belongs to the theory of $f(R,T)$ gravity, Model II belongs to the theory of $f(R)$ gravity and Model III is a combination of Models I and II. These functions have been taken into account for the exploration of wormhole solutions. The shape function, a wormhole metric function, is newly defined which satisfies the flare out condition. Further, the stability condition and energy conditions, namely null, weak and dominant energy conditions, have been examined with respect to each model.

In this paper, we obtain an exact spherically symmetric wormhole solution with anisotropic matter distribution in the regularized four-dimensional (4D) Einstein Gauss–Bonnet gravity (4D EGB). Recently, a new attempt has been made to include nontrivial contributions of Gauss–Bonnet term to the gravitational dynamics by regularizing EGB gravity in $4$-dimensions. To find the exact solution of the wormhole geometry, we studied two specific radial-dependent shape functions $b(r)=r_0{(\frac{cosh(r_0)}{cosh(r)})}^{\mu }$, $0<\mu <1$ and $b(r)=r_0(\frac{a^r}{a^{r_0}})$, $0<a<1$ in the context of 4D EGB gravity. For each shape function, we find the exact wormhole solution and analyze the properties of wormhole existence graphically. The anisotropic parameter, equation of state (EoS) and energy conditions are tested graphically for each shape function. The behavior of both shape functions is thoroughly evaluated with the throat radius $r=r_0=1$. Specifically, we recovered the original results exactly to 4D Morris–Throne wormholes of General Relativity by simply imposing the limit as $\alpha \to 0$ and comparison has been done between the branch results in 4D EGB gravity and General Relativity by graphical point of view.

In this paper, we derive the exact solution of traversable wormholes illustrating spherically symmetric geometry with anisotropic matter distribution entering the throat in the formalism of $f({ℛ},{𝒯})$ gravity, where ${ℛ}$ is Ricci scalar and ${𝒯}$ is trace of energy–momentum tensor. For this purpose, we assume a power law-type generic function $f({ℛ},{𝒯})={ℛ}+\gamma {{ℛ}}^2+\alpha {𝒯}$, where $\gamma$ and $\alpha$ are being constants, with two different choices of shape functions $a(r)=r_0(\frac{b^r}{b^{r_0}}),0<a(r)<1$ and $a(r)=r_0{(\frac{cosh(r_0)}{cosh(r)})}^{\mu },0<\mu <1$. For each approach, we find the exact solution and studied the existence of wormhole solutions in the presence of exotic and non-exotic matter. The graphical behavior of equation of state (EoS) parameter and energy condition bounds is also investigated for each shape function. The realistic wormhole solutions are obtained for the shape functions which satisfy necessary conditions at the throat radius $r=r_0=1$. Finally, we observe that there is small deviation in the results obtained by General Relativity and $f({{ℛ}}^2,{𝒯})$ gravity.

In this work, static traversable wormholes are investigated in the context of $f(R,L_m)$ gravity theory. Considering $f(R,L_m)=a{R}^2+cR+d{L}_m$ model (in which $a,c$ and $d$ are constants) and assuming $2\rho +p_r+2p_t=0$, a new shape function is obtained which is not asymptotically flat, but satisfies all the conditions of a shape function. Also in this case, all energy conditions (except strong energy conditions) are satisfied. Assuming $f(R,L_m)=L_m{R}^2$ and shape function $b(r)=\frac{r_0^2}{r}$, a new energy density function is obtained. Finally, a comparative study of ECs is investigated for different shape functions under the assumption $\rho =q{(\frac{r}{r_0})}^{-n}$ and $f(R,L_m)=k{L}_m{R}^{1+1.5w}$ (where $k$, $w$ and $q$ are constants) and we have seen that the presence of exotic matter is not required in most of the cases.