Evolving Wormholes in a Cosmological Background

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.

We obtain Traversable Wormholes in the 4D Einstein-Gauss-Bonnet (4D-EGB) gravity with phenomenological Bose-Einstein Condensates (BEC) dark matter. The 4D-EGB gravity considered here results from a regularization of the higher-dimensional EGB gravity in the limit $D \to 4$. The rescaled Gauss-Bonnet coupling parameter ($\alpha$) plays an important role to admit spherically symmetric traversable wormholes (TW). Considering the energy density profile of non-relativistic BEC matter, the shape function of the TW geometry is determined. Thereafter, all the energy conditions namely, Null energy condition (NEC), Strong energy condition, Weak energy condition, and Dominant energy condition are analyzed for a constant redshift function. The flaring-out and asymptotic flatness conditions are probed for a realistic scenario. The embedding diagram of the TW is also analyzed along with proper radial distance, volume integral quantifier, and pressure anisotropy. TW obtained here are found stable at the throat when $\alpha = - 0.0512471$ with a set of model parameters, which are determined from the acceptable sound speed measurement. In the 4D Einstein-Gauss-Bonnet (EGB) gravity, all the energy conditions are satisfied for $\alpha \in [-4.222,-4]$ with a set of model parameters. There is a range of $\alpha$ for which exotic properties of the BEC DM is not needed to sustain the TW throat, which is a new observation in modified 4D EGB gravity with BEC Dark Matter profile.

A class of traversable wormholes in the Starobinsky-like [formula omitted] gravity with anisotropic dark matter

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.

A traversable wormhole, which is a class of wormholes in general relativity (GR), was proposed by Morris and Thorne in 1988. However, its existence requires the exotic matter violating the energy conditions. This thesis examines the wormhole solutions in the theory of massive gravity, focusing only on the de Rham, Gabadadze and Tolley (dRGT) theory of massive gravity which is the nonlinear massive gravity without ghost and quantify the wormhole solutions. We construct the wormhole solutions in context of the modified GR, investigate their stability, and examine the conditions of the exotic matter. Two methods for wormhole constructions are applied i.e., the Lorentzian traversable and thin-shell wormholes. We found that the wormholes in dRGT massive gravity require the exotic matter only near their throats not spreading all the Universe like in GR.

A possible astrophysical object to be found in General Relativity is the wormhole. This special solution describes a topological bridge connecting points in two distinguished universes or two different points in the same universe. Despite it was never observed so far, is desired to find traversable wormholes, i.e., wormholes which have a throat at which there is no horizon. However, the traversable wormhole constraints yield solutions that violate all the energy conditions in general relativity. In the last few years, several models to describe gravity beyond $$\Lambda $$ CDM have been proposed. Then, it is relevant to look for wormhole solutions for these new theories. In this study, we are going to unveil new wormhole solutions for the so-called f(Q, T) gravity. This theory of gravity is based on the non-metricity scalar Q, which is responsible for the gravitational interaction together with the energy-momentum trace T. We use the embedding procedure to find both the energy and the equilibrium conditions for the existence of wormholes. Then, the nontrivial contributions coming from f(Q, T) gravity are embedded into the effective equations for density and pressures. We also considered the presence of strange matter in the wormhole throat. Such a matter obeys the notorious MIT bag Model. We are going to present new scenarios confirming the viability of traversable wormholes in f(Q, T) gravity with the strange matter, satisfying SEC and WEC energy conditions.

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.

In this paper, we consider the Einstein–Gauss–Bonnet gravity in the presence of power Maxwell invariant field and present a class of rotating magnetic solutions. These solutions are nonsingular and horizonless, and satisfy the so-called flare-out condition at r = r+ and may be interpreted as traversable wormhole near r = r+. In order to have a vanishing electromagnetic field at spatial infinity, we restrict the nonlinearity parameter to s > 1/2. Investigation of the energy conditions shows that these solutions satisfy the null, week, and strong energy conditions simultaneously for s > 1/2, which means that there is no exotic matter near the throat. We also calculate the conserved quantities of the wormhole such as mass, angular momentum, and electric charge density, and show that the electric charge depends on the rotation parameters and the static wormhole does not have a net electric charge density. In addition, we show that for s = (n + 1)/4, the energy–momentum tensor is traceless and the solutions are conformally invariant, in which the expression of the Maxwell field does not depend on the dimensions and its value coincides with the Reissner–Nordström solution in four dimensions. Finally, we produce higher dimensional BTZ-like wormhole solutions for s = n/2, in which in this case the electromagnetic field Fψr∝r−1.

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 this study, we investigate anisotropic Bianchi Type VI cosmological model within the framework of fractal universe. By utilizing the energy–momentum tensor for a perfect fluid, we solve the corresponding field equations. In this study, we derive leading cosmological parameters, including the hubble parameter H and deceleration parameter q in terms of cosmic time and redshift also. To determine the model parameters such as k, [Formula: see text] and the hubble constant [Formula: see text], the hubble dataset was analyzed using the [Formula: see text] test. This analysis reveals the best-fit values of [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] match with the [Formula: see text]CDM model. We carry blow-by-blow analysis of the model’s characteristics via energy density [Formula: see text], pressure p and EoS parameter. We examine whether the energy conditions — null energy condition (NEC), strong energy condition (SEC), weak energy condition (WEC) and dominant energy condition (DEC) — are satisfied. Furthermore, the diagnostic parameters are analyzed to evaluate the deviation of the obtained model from the [Formula: see text]CDM model and to classify various dark energy models during the universe’s expansion. The om diagnostic is depicted as a function of redshift for [Formula: see text] and [Formula: see text] revealing that [Formula: see text] settles around [Formula: see text] with slight deviation in the range [Formula: see text]. The model closely aligns with [Formula: see text]CDM at higher redshifts. The pair of statefinder diagnostics r versus s is also discussed, and our model for [Formula: see text] represents the [Formula: see text]CDM model.

In the context of current scenario, it is crucial to look beyond Einstein’s theory, which opens the door to certain modified theories of gravity. So, present study is devoted to investigate the various energy conditions, particularly, strong energy condition (SEC), weak energy condition (WEC), null energy condition (NEC) and dominant energy condition (DEC) corresponding to different functional forms of f(R) gravity. We have studied for flat, isotropic and homogeneous FLRW cosmological model filled with interacting field i.e., perfect fluid is coupled with mass less scalar field for different models of modified f(R) gravity in which R is the Ricci scalar. We have observed, the accelerated expansion of the Universe which exact match with recent observational evidences.

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.

In general relativity, traversable wormholes are possible provided they do not represent shortcuts in the spacetime. Einstein equations, together with the achronal averaged null energy condition, demand to take longer for an observer to go through the wormhole than through the ambient space. This forbids wormholes connecting two distant regions in the space. The situation is different when higher-curvature corrections are considered. Here, we construct a traversable wormhole solution connecting two asymptotically flat regions, otherwise disconnected. This geometry is an electro-vacuum solution to Lovelock theory of gravity coupled to an Abelian gauge field. The electric flux suffices to support the wormhole throat and to stabilize the solution. In fact, we show that, in contrast to other wormhole solutions previously found in this theory, the one constructed here turns out to be stable under scalar perturbations. We also consider wormholes in AdS. We present a protection argument showing that, while stable traversable wormholes connecting two asymptotically locally AdS$_5$ spaces do exist in the higher-curvature theory, the region of the parameter space where such solutions are admitted lies outside the causality bounds coming from AdS/CFT.

This research work discusses the energy bounds in [Formula: see text] gravity with an anisotropic background, where [Formula: see text] is the Ricci scalar and [Formula: see text] is the trace of the energy–momentum tensor. For our study, we consider the locally rotationally symmetric Bianchi Type-I space-time. Moreover, we calculate the field equations and find exact solutions by considering different [Formula: see text] gravity models. We investigate the graphical behavior of energy density and pressure components by considering these distinct gravity models. We further use Hubble, deceleration, jerk, and snap parameters to evaluate the viability of our models. We also perform the graphical analysis to observe the behavior of energy conditions especially null energy conditions, weak energy conditions, strong energy conditions, and dominant energy conditions. It can be noticed that all considered [Formula: see text] gravity models support the idea of the presence of exotic matter, which justifies the phenomenon of expansion of the universe.

All known solutions to the Einstein equations describing rotating cylindrical wormholes lack asymptotic flatness and therefore cannot describe wormhole entrances as local objects in our Universe. To overcome this difficulty, wormhole solutions are joined to flat asymptotic regions at some surfaces $\Sigma_-$ and $\Sigma_+$. The whole configuration thus consists of three regions, the internal one containing a wormhole throat, and two flat external ones, considered in rotating reference frames. Using a special kind of anisotropic fluid respecting the Weak Energy Condition (WEC) as a source of gravity in the internal region, we show that the parameters of this configuration can be chosen in such a way that matter on both junction surfaces $\Sigma_-$ and $\Sigma_+$ also respects the WEC. Closed timelike curves are shown to be absent by construction in the whole configuration. It seems to be the first example of regular twice asymptotically flat wormholes without exotic matter and without closed timelike curves, obtained in general relativity.