Embedding procedure and wormhole solutions in Rastall gravity utilizing the class I approach

We study new solutions of black bounce spacetimes formulated in $f(T)$ gravity in four dimensions. First, we present the case of a diagonal tetrad, where a constraint arises in the equations of motion, which is divided into the cases of null torsion, constant torsion, and Teleparallel. The Null Energy Condition (NEC) is still always violated, which implies that the other energy conditions are violated. The solutions are regular in all spacetime and the solution with null torsion exhibits discontinuity between the energy conditions outside and inside the event horizon. Second, we present the case of non-diagonal tetrads. This case is divided into a Simpson-Visser type model and a quadratic model. The NEC continues to be violated, implying a violation of the other energy conditions. The solutions are regular in all spacetimes. An interesting result is that due to the possibility that the area associated with the metric is different from $4\pi r^2$, the no-go theorem established in the usual $f(T)$ is violated, appearing the new possibility $g_{00}=-g^{11}$, for the components of the metric.

In this work, we have studied how incorporating viscous fluids leads to exact bounce cosmological solutions in general relativity (GR) framework. Specifically, we propose a novel parameterization of bulk viscosity coefficient of the form [Formula: see text], where [Formula: see text], with [Formula: see text] being some positive constants and [Formula: see text] being the bounce epoch. We investigate how this form of bulk viscosity may assist in explaining the early universe’s behavior, with a particular focus on non-singular bounce scenario by studying the various energy conditions and other related cosmological observables and how the model parameters affect the evolution of the Universe. We demonstrate that the null energy conditions (NEC) and strong energy conditions (SEC) violation occurs at the bounce point while dominant energy conditions (DEC) is satisfied. Finally, we carried out a stability check based on linear order perturbation to the Hubble parameter. We found that the perturbation vanishes asymptotically at later times, which indicates a stable behavior of the bounce scenario.

A fundamental ingredient in wormhole physics is the presence of exotic matter, which involves the violation of the null energy condition. Although a plethora of wormhole solutions have been explored in the literature, it is useful to find geometries that minimize the usage of exotic matter. In this work, we find exact wormhole solutions in Brans–Dicke theory where the normal matter threading the wormhole satisfies the null energy condition throughout the geometry. Thus, the latter implies that it is the effective stress–energy tensor containing the scalar field, that plays the role of exotic matter, that is responsible for sustaining the wormhole geometry. More specifically, we consider a zero redshift function and a particular choice for the scalar field and determine the remaining quantities, namely, the stress–energy tensor components and the shape function. The solution found is not asymptotically flat, so that this interior wormhole spacetime needs to be matched to an exterior vacuum solution.

Casimir wormhole solutions in [formula omitted] gravity

Wormhole solutions in General Relativity (GR) require exotic matter sources that violate the null energy condition (NEC), and it is well-known that higher-order modifications of GR and some alternative matter sources can support wormholes. In this study, we explore the possibility of formulating traversable wormholes in f (R) modified gravity, which is perhaps the most widely discussed modification of GR, with two approaches. First, to investigate the effects of geometrical constraints on the global characteristics, we gauge the rr–component of the metric tensor and employ Padè approximation to check whether a well–constrained shape function can be formulated in this manner. We then derive the field equations with a background of string cloud and numerically analyse the energy conditions, stability, and amount of exotic matter in this space-time. Next, as an alternative source in a simple f (R) gravity model, we use the background cloud of strings to estimate the wormhole shape function and analyse the relevant properties of the space-time. These results are then compared with those of wormholes threaded by normal matter in the simple f (R) gravity model considered. The results demonstrate that string cloud is a viable source for wormholes with NEC violations; however, the wormhole space-times in the simple f (R) gravity model considered in this study are unstable.

Existence of static wormhole solutions using [formula omitted] theory of gravity

In this study, we explore the geometric features of a charged traversable wormhole (WH) in the realm of [Formula: see text] gravity with strange quark matter. We developed the field equations for Morris–Thorne-type charged WH metric with anisotropic fluid distribution and obtained the corresponding WH results for two kinds of shape functions. To visualize the proper shape of the WH, we depicted three-dimensional and two-dimensional embedding portraits for the chosen values of both [Formula: see text] and [Formula: see text] at the throat radius [Formula: see text]. In addition, all necessary needs to build a WH shape are analyzed for the considering shape functions. Next, we analyze the energy conditions together with the MIT bag model, for different values of free parameters for both cases. It is observed that in both cases, all the energy conditions are violated in different regions of the WH spacetime, corresponding to some ranges of model parameters. The violation of the null energy condition (NEC) confirms the existence of exotic matter inside the WH throat. On the other hand, the validity of energy conditions predicts a fabric of stable traversable WHs. For both cases, the equilibrium configuration is analyzed through the TOV equation showing the stability of considering solutions.

This article investigates the properties of a wormhole model in a specific gravity theory, namely f(Ric, T) = Ric + 2λ T. The wormhole solution is analyzed using an exponential shape function. The study examines various parameters, such as density, radial pressure, transverse pressure, equation-of-state parameters, and energy conditions, within the framework of deformed gravity. The research emphasizes the influence of the parameter λ on energy condition violations and the equilibrium state of the Finslerian wormhole solution. These effects are attributed to anisotropic and hydrostatic forces present in modified gravity. The study demonstrates that the gravity model effectively captures the characteristics of wormholes within the Finslerian space-time. Additionally, the identified features of the wormhole are utilized to visualize its structure by creating a three-dimensional representation of the embedded surface. In summary, this research contributes to understanding wormholes in modified gravity theories, highlighting the importance of the parameter λ in determining their behavior and properties.

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 [Formula: see text] theory of gravity proposed by Harko et al. [Phys. Rev. D 84 (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 isotropic loop quantum cosmology, non-perturbatively modified dynamics of a minimally coupled scalar field violates weak, strong and dominant energy conditions when they are stated in terms of the equation-of-state parameter. The violation of the strong energy condition helps to have non-singular evolution by evading singularity theorems thus leading to a generic inflationary phase. However, the violation of weak and dominant energy conditions raises concern, as in general relativity these conditions ensure causality of the system and stability of vacuum via the Hawking–Ellis conservation theorem. It is shown here that the non-perturbatively modified kinetic term contributes negative pressure but positive energy density. This crucial feature leads to the violation of energy conditions but ensures the positivity of energy density, as the scalar matter Hamiltonian remains bounded from below. It is also shown that the modified dynamics restricts group velocity for inhomogeneous modes to remain sub-luminal thus ensuring causal propagation across spatial distances.

We explore the possibility of traversable wormhole formation in the dark matter halos in the context of f(Q) gravity. We obtain the exact wormhole solutions with anisotropic matter source based on the Bose–Einstein condensate, Navarro-Frenk-White, and pseudo-isothermal matter density profiles. Notably, we present a novel wormhole solution supported by these dark matters using the expressions for the density profile and rotational velocity along with the modified field equations to calculate the redshift and shape functions of the wormholes. With a particular set of parameters, we demonstrate that our proposed wormhole solutions fulfill the flare-out condition against an asymptotic background. Additionally, we examine the energy conditions (ECs), focusing on the null ECs at the wormhole’s throat, providing a graphical representation of the feasible and negative regions. Our study also examines the wormhole’s shadow in the presence of various dark matter models, revealing that higher central densities result in a shadow closer to the throat, whereas lower values have the opposite effect. Moreover, we explore the deflection of light when it encounters these wormholes, particularly noting that light deflection approaches infinity at the throat, where the gravitational field is extremely strong.

Wormholes are non-trivial topological structures that arise as exact solutions to Einstein’s field equations, theoretically connecting distinct regions of spacetime via a throat-like geometry. While static traversable wormholes necessarily require exotic matter that violates the classical energy conditions, subsequent studies have sought to minimize such violations by introducing time-dependent geometries embedded within cosmological backgrounds. This review provides a comprehensive survey of evolving wormhole solutions, emphasizing their formulation within both general relativity and alternative theories of gravity. We explore key developments in the construction of non-static wormhole spacetimes, including those conformally related to static solutions, as well as dynamically evolving geometries influenced by scalar fields. Particular attention is given to the wormholes embedded into Friedmann–Lemaître–Robertson–Walker (FLRW) universes and de Sitter backgrounds, where the interplay between the cosmic expansion and wormhole dynamics is analyzed. We also examine the role of modified gravity theories, especially in hybrid metric–Palatini gravity, which enable the realization of traversable wormholes supported by effective stress–energy tensors that do not violate the null or weak energy conditions. By systematically analyzing a wide range of time-dependent wormhole solutions, this review identifies the specific geometric and physical conditions under which wormholes can evolve consistently with null and weak energy conditions. These findings clarify how such configurations can be naturally integrated into cosmological models governed by general relativity or modified gravity, thereby contributing to a deeper theoretical understanding of localized spacetime structures in an expanding universe.

In this paper, we study the traversable wormhole solutions for a logarithmic corrected [Formula: see text] model by considering two different statements of shape [Formula: see text] and redshift [Formula: see text] functions. We calculate the parameters of the model including energy density [Formula: see text], tangential pressure [Formula: see text] and radial pressure [Formula: see text] for the corresponding forms of the functions. Then, we investigate different energy conditions such as null energy condition, weak energy condition, dominant energy condition and strong energy condition for our considered cases. Finally, we explain the satisfactory conditions of energy of the models by related plots.

Ellis–Bronnikov (EB) wormholes require violation of null energy conditions at the ‘throat’. This problem was cured by a simple modification of the ‘shape function’, which introduces a new parameter mge 2 (m=2 corresponds to the EB model). This leads to a generalised (GEB) version. In this work, we consider a model where the GEB wormhole geometry is embedded in a five dimensional warped background. We studied the status of all the energy conditions in detail for both EB and GEB embedding. We present our results analytically (wherever possible) and graphically. Remarkably, the presence of decaying warp factor leads to satisfaction of weak energy conditions even for the EB geometry, while the status of all the other energy conditions are improved compared to the four dimensional scenario. Besides inventing a new way to avoid the presence of exotic matter, in order to form a wormhole passage, our work reveals yet another advantage of having a warped extra dimension.

In this work, we intend to explore wormhole geometries in the framework of f(R,Lm) gravity. We derive the field equations for the generic f(R,Lm) function by assuming the static and spherically symmetric Morris–Thorne wormhole metric. Then we consider two non-linear f(R,Lm) model, specifically, f(R,Lm)=R2+Lmα and f(R,Lm)=R2+(1+λR)Lm, where α and λ are free model parameters. We obtain the wormhole solutions by assuming three cases, namely, a linear barotropic EoS, anisotropic EoS, and isotropic EoS corresponding to model I. We observe that for both barotropic and anisotropic cases, the corresponding wormhole solutions obey the flaring-out condition under asymptotic background, while for the isotropic case, the shape function does not follow the flatness condition. Also, we find that the null energy condition exhibits negative behavior in the vicinity of the throat. Further, we consider two different shape functions to investigate the behavior of model II. We find some constraints on the model parameter for which the violation of the null energy condition exhibits. Finally, we employ the volume integral quantifier to calculate the amount of exotic matter required near the wormhole throat for both models. We conclude that the modification of standard GR can efficiently minimize the use of exotic matter and provide stable traversable wormhole solutions.