Thorne Wormhole Research Articles

Dynamics of dissipative gravitational collapse in the Morris–Thorne wormhole metric: One scenario - several outcomes

We consider the dynamical Morris–Thorne metric with radiating heat flow. By matching the interior Morris–Thorne metric with an exterior Vaidya metric we trace out the collapse solutions for the corresponding spherically symmetric inhomogeneous distribution of matter. The solutions obtained are broadly of four different types, giving different end state dynamics. Corresponding to three of the solutions we elaborate the collapsing dynamics of the Morris–Thorne type evolving wormhole. We show that for all those cases where collapse upto zero proper volume is obtained in finite time, the ensuing singularity is always a black hole type. However our solutions can also show other end states, like oscillating wormhole-black hole pair or infinite time contracting universe or a conformal past matter dominated universe. In all the cases we have worked out the background dynamics and physics of the solution. All our solutions are illustrated with appropriate graphical descriptions.

Solution of Weyl–Lanczos relations for Morris–Thorne wormhole

Solution of Weyl–Lanczos relations for Morris–Thorne wormhole

Possible existence of traversable wormhole in Finsler–Randers geometry

In the present article, we have explored the possible existence of a traversable wormhole in the framework of Finsler–Randers (F–R) geometry. In order to achieve this goal, first, we have constructed gravitational field equations for static, spherically symmetric spacetime with anisotropic fluid distribution in F–R geometry. Next, we have written the deduced form of field equations in the background of Morris–Thorne wormhole geometry. To visualize the shape of the wormhole, we have selected exponential shape function b(r)=frac{r}{expleft( eta left( frac{r}{r_{0}} - 1right) right) } with the constant parameter eta and the throat radius r_{0} and depicted two-dimensional and three-dimensional embedding diagrams corresponding to some considered values of eta and r_{0}. Moreover, all essential requirements to build a wormhole shape have been examined for the reported shape function. Next, We have analyzed wormhole configuration for three cases (I, II, III) corresponding to three selected redshift functions. Furthermore, each case is analyzed by dividing it into two models such as (i) Model-1 (for general anisotropic EoS p_{t}=chi p_{r}) and (ii) Model-2 (for linear phantom-like EoS p_{r} + omega rho =0). In each model of three cases, we have verified the validity of the wormhole solution in F–R geometry by considering null, weak, strong and dominant energy conditions. Also, the total amount of averaged NEC-violating matter near the wormhole throat has been analyzed by computing volume integral quantifier.

Traversable Morris–Thorne–Buchdahl wormholes in quadratic gravity

The special Buchdahl-inspired metric obtained in a recent paper [Phys. Rev. D 107, 104008 (2023)] describes asymptotically flat spacetimes in pure mathcal {R}^{2} gravity. The metric depends on a new (Buchdahl) parameter tilde{k} of higher-derivative characteristic, and recovers the Schwarzschild metric when tilde{k}=0. It is shown that the special Buchdahl-inspired metric supports a two-way traversable Morris–Thorne wormhole for tilde{k}in (-1,0) in which case the Weak Energy Condition is formally violated, a naked singularity for tilde{k}in (-infty ,-1)cup (0,+infty ), and a non-Schwarzschild structure for tilde{k}=-1.

Wormhole solutions in [formula omitted] gravity

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.

Some aspects of Morris–Thorne wormhole in Scalar–Tensor theory

In this work, we reach the equations of motion of Morris–Thorne wormhole geometry by means of the Einstein Field Equations and Klein–Gordon Equation of Scalar–Tensor Theory. We discuss the anisotropic matter energy distribution. We determine a relation between the radial and the transverse pressures. Hence, we express the anisotropic energy–momentum tensor in terms of one pressure class, by means of that relation. Besides that, we check the isotropic case and show that there is no traversable wormhole (WH), in the zero redshift function situation, if the energy–momentum distribution of the universe is isotropic. In addition, we represent the conditions in order that the Null Energy Condition (NEC) is satisfied in the zero redshift function case, for anisotropic distribution. We also propose a special class of traversable WH shape functions. We will be calling the WHs corresponding to that class of functions as the Yukawa Type WHs. We expressed the NEC for those WHs particularly. Furthermore, we determine the radial and the transverse pressures in zero redshift function situation.

The shadow of charged traversable wormholes

In this paper, we compute the shadow cast by a charged Morris–Thorne wormhole when the light source is a star located beyond the mouth which is opposite to the observer. First, we provide an extensive analysis of the geodesic properties of the spacetime, both for null and massive particles. The geometrical properties of this solution are such that independently of the viewing angle, some light rays always reach the observer. Additionally, the structure of the images is preserved among the different values of the charge and scales proportionally to the charge value.

Gravitational lensing for wormhole with scalar field in f(R) gravity

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 [Formula: see text] and relativistic Einstein ring [Formula: see text] 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.

Non-commutative wormholes in [formula omitted] gravity satisfying the energy conditions

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 redshift functions. First, we use well constrained metric and model parameters in a viable f(R) gravity model to demonstrate that wormholes respecting the NEC can be obtained with suitable choices of parameters. Additionally, we check the strong and dominant energy conditions to further validate our results. We then leverage non-commutative geometry in the framework of f(R) gravity to show that wormholes respecting the different energy conditions with a phantom-like source can be realized with suitable choices of model parameters. Our comprehensive analyses using well-constrained model parameters show that wormholes satisfying the NEC can be realized in the framework of non-commutative geometry with modified gravity.

Accretions of (m, n)-type Pilgrim dark energies with logarithmic and power-law entropy corrections onto (D + 2)-dimensional black hole and wormhole

This work aims to study the accretions of dark energy coupled with dark matter onto a static Schwarzschild black hole of [Formula: see text] dimensions. Besides the accretion of fluids, the effect due to evaporation of black hole of [Formula: see text] dimensions is under consideration. Mass is one of the interesting dynamical properties of a black hole. The changes in masses have been projected in the framework of the Friedmann–Robertson–Walker model of the universe of [Formula: see text] dimensions. The [Formula: see text]-type Pilgrim dark energies with their logarithmic and power-law entropy corrections are considered as the form of dark energy in our study. Further, the scale factor that is considered as [Formula: see text], [Formula: see text] follows the power-law form. The changes in the dynamical mass of the black hole have been calculated with the variation corresponding to redshift [Formula: see text] while dark matter and specified type of dark energy accrete onto [Formula: see text]-dimensional Schwarzschild black hole. It is found that the dynamical mass of the black hole increases in the late-time epoch as a consequence of the prescribed form of dark energy accretion and evaporation of the black hole. Finally, we discuss the accretion phenomena of the above-specified types of dark energies onto [Formula: see text]-dimensional Morris–Thorne wormhole. It has been investigated that the masses of the black hole and the wormhole sensitively vary with the values of the dimensions.

Landau–Lifshitz and Weinberg Energy Distributions for the Static Regular Simpson–Visser Space-Time Geometry

The symmetric Landau–Lifshitz and Weinberg energy–momentum complexes are utilized in order to determine the energy distribution in a four-dimensional, static and spherically symmetric regular Simpson–Visser space-time geometry. For different values of the metric parameter a, the static Simpson–Visser space-time geometry corresponds to the Schwarzschild black hole solution, to a regular black hole solution with a one-way spacelike throat, to a one-way wormhole solution with an extremal null throat, or to a traversable Morris–Thorne wormhole solution. Both symmetric prescriptions yield a zero momentum, while the energy distributions calculated have an expression dependent on the mass m, the radial coordinate r, and the metric parameter a. Some special limiting cases of the results derived are considered, while a possible astrophysical application to questions of gravitational lensing is indicated.

Phantom energy-supported wormhole model in f(R,T) gravity assuming conformal motion

In this article, we have discussed Morris and Thorne (MT) wormhole solutions in a modified theory of gravity that admits conformal motion. Here, we explore the wormhole solutions in [Formula: see text] gravity, which is a function of the Ricci scalar ([Formula: see text]) and the trace of the stress–energy tensor ([Formula: see text]). To study wormhole geometries, we make assumption of spherical symmetric static spacetime and the existence of conformal Killing symmetry to get more acceptable astrophysical outcomes. To do this, we choose the expression of [Formula: see text] as [Formula: see text]. Here, we employ the phantom energy EoS relating to radial pressure and density given by [Formula: see text] with [Formula: see text] to constrain our model. Following a discussion of wormhole geometry and behavior of shape function, the study moves on to the computation of proper radial distance, active mass function, the nature of total gravitational energy and a discussion on the violation of energy conditions. We have shown that the wormhole solutions exist for positive as well as negative values of the coupling constant [Formula: see text]. From our analysis, we see that no wormhole solution exists for [Formula: see text]. All the physical parameters have been drawn by employing the values of [Formula: see text] as [Formula: see text] and [Formula: see text], where [Formula: see text] corresponds to general relativity (GR) case. It is found that for our proposed model, a realistic wormhole solution satisfying all the properties can be obtained.

Deflection angle for charged wormhole in f(R,T) gravity

This paper is focused on the study of charged wormholes which are combinations of Morris–Thorne wormhole and Reissner–Nordström spacetime. Gravitational lensing is an important tool which has been adopted to detect various objects like wormholes using the notion of deflection angle. In this work, we have evaluated deflection angle with and without using the strong field limit coefficients and compared the results. Further, exact charged wormhole solutions are obtained in [Formula: see text] gravity and the nature of the energy conditions is examined.

Accretions of Tsallis, Rényi and Sharma–Mittal dark energies onto higher-dimensional Schwarzschild black hole and Morris–Thorne wormhole

In this work, we study the dark energy accretion phenomena onto [Formula: see text]-dimensional Schwarzschild black hole and [Formula: see text]-dimensional Morris–Thorne wormhole. We obtain the [Formula: see text]-dimensional Schwarzschild black hole mass and [Formula: see text]-dimensional Morris–Thorne wormhole mass and their rate of change of masses due to accretion. For the dark energy component, we consider Tsallis, modified Rényi and “modified” Sharma–Mittal holographic dark energy (HDE) and new agegraphic dark energy (NADE). We also find the black hole mass and the wormhole mass in terms of redshift when cold dark matter and the specified forms of dark energies accrete onto them. In most cases, the black hole mass increases, and wormhole mass decreases for HDE and NADE accretions. The only exception is the Sharma–Mittal NADE, where the black hole mass decreases and wormhole mass increases during the evolution of the Universe. However, the slope of increasing/decreasing mass significantly depends on the dimension in almost all cases.

Dynamics in wormhole spacetimes: a Jacobi metric approach

This article deals with the study of the dynamics of particles in different wormhole geometries. Using the Jacobi metric approach we study the geodesic motion on the Morris–Thorne wormhole. We found the only stable circular orbit located at the throat. We show that the Gaussian curvature of the Jacobi metric is directly related with the wormhole flare-out condition. We provide a simple test for determining the existence of a throat in a spacetime by using the Gaussian curvature of the associated Jacobi metric only. We discuss about the trajectories in the Kepler problem in a wormhole background. Finally, we discuss about the restrictions over the stress–energy tensor imposed by the existence of elliptic orbits in the Kepler problem.

Morris–Thorne wormhole with Karmarkar condition

In this paper, we construct a wormhole shape function by using Karmarkar condition. We observe that our proposed shape function connects two asymptotically flat regions, which shows the existence of Morris–Thorne traversable wormhole. Moreover, we also represent the embedding diagram in three-dimensional Euclidean space which can be extended from throat to infinity. Further, the Null and Weak energy conditions are discussed in detail. With this shape function, the anisotropic factor exhibits a repulsive nature at the throat. We support all the analysis of this work through graphical representation. It is concluded that our proposed model fulfills all the necessary conditions and shows the existence of exotic matter in the formulism of wormhole geometry in the context of General Relativity.

The gravitational perturbation of a Morris–Thorne wormhole and the Newman–Penrose formalism

The gravitational perturbation of the Morris–Thorne wormhole has been derived by using the Newman–Penrose formalism. We apply the Teukolsky equation to the wormhole spacetime, compute the perturbed Weyl scalars, and obtain its master equation, decomposed in spin weighted spherical harmonics with spin weight −2. For simplicity, we consider the perturbation provoked by a single Gaussian pulse of pressureless dust matter.

Echoes from the scattering of wavepackets on wormholes

It has been recently shown that observing pulses isolated from the gravitational radiation transient (also known as echoes) would prove the existence of exotic compact objects (ECOs). Many features of the ringdown signal can be reproduced by simulating a scattering problem instead of the full coalescence of ECOs. In this paper, we study the dynamics of scalar and tensor wavepackets colliding against a spherically symmetric Morris–Thorne wormhole. Our aim is to extract the features of the time-dependent scattering solutions inside and outside the effective potential cavity in addition to their asymptotic behavior. Using the geometrical optics approximation, we show that the amplitude of the echoes is only large enough in a narrow bandwidth of frequency space. Additionally, we show that the cavity modifies the polarization of the asymptotic gravitational wave solutions. The computer code used to produce these results is publicly available for further applications, including scattering and accretion processes.

Wormholes with ρ(R, R′) matter in f(R, T) gravity

Models of static wormholes are investigated in the framework of $f(R,T)$ gravity (where $R$ is the curvature scalar and $T$ is the trace of the energy-momentum tensor). An attempt to link the energy density of the matter component to the Ricci scalar is made, which for the Morris and Thorne wormhole metric with constant redshift function yields $R(r)=2{b}^{\ensuremath{'}}(r)/{r}^{2}$. Exact wormhole solutions are obtained for three particular cases when $f(R,T)=R+2\ensuremath{\lambda}T$: $\ensuremath{\rho}(r)=\ensuremath{\alpha}R(r)+\ensuremath{\beta}{R}^{\ensuremath{'}}(r)$, $\ensuremath{\rho}(r)=\ensuremath{\alpha}{R}^{2}(r)+\ensuremath{\beta}{R}^{\ensuremath{'}}(r)$, and $\ensuremath{\rho}(r)=\phantom{\rule{0ex}{0ex}}\ensuremath{\alpha}R(r)+\ensuremath{\beta}{R}^{2}(r)$. Additionally, traversable wormhole models are obtained for the two first cases. However, when the wormhole matter energy density is of the third type, only solutions with constant shape correspond to traversable wormholes. Exact wormhole solutions possessing the same properties can be constructed when $\ensuremath{\rho}=\ensuremath{\alpha}R(r)+\ensuremath{\beta}{R}^{\ensuremath{-}2}(r)$, $\ensuremath{\rho}=\ensuremath{\alpha}R(r)+\ensuremath{\beta}r{R}^{2}(r)$, $\ensuremath{\rho}=\ensuremath{\alpha}R(r)+\ensuremath{\beta}{r}^{\ensuremath{-}1}{R}^{2}(r)$, $\ensuremath{\rho}=\ensuremath{\alpha}R(r)+\phantom{\rule{0ex}{0ex}}\ensuremath{\beta}{r}^{2}{R}^{2}(r)$, $\ensuremath{\rho}=\ensuremath{\alpha}R(r)+\ensuremath{\beta}{r}^{3}{R}^{2}(r)$, and $\ensuremath{\rho}=\ensuremath{\alpha}{r}^{m}R(r)\mathrm{log}(\ensuremath{\beta}R(r))$, as well. On the other hand, for $f(R,T)=R+\ensuremath{\gamma}{R}^{2}+2\ensuremath{\lambda}T$ gravity, two wormhole models are constructed, assuming that the energy density of the wormhole matter is $\ensuremath{\rho}(r)=\ensuremath{\alpha}R(r)+\ensuremath{\beta}{R}^{2}(r)$ and $\ensuremath{\rho}(r)=\ensuremath{\alpha}R(r)+\ensuremath{\beta}{r}^{3}{R}^{2}(r)$, respectively. In this case, the functional form of the shape function is taken to be $b(r)=\sqrt{{\stackrel{^}{r}}_{0}r}$ (where ${\stackrel{^}{r}}_{0}$ is a constant) and the possible existence of appropriate static traversable wormhole configurations is proven. The explicit forms of the pressures ${P}_{r}$ and ${P}_{l}$ leading to this result are found in both cases. As a general feature, the parameter space can be divided into several regions according to which of the energy conditions are valid. These results can be viewed as an initial step towards using specific properties of the new exact wormhole solutions to propose new functional forms for describing the matter content of wormholes.

Globally Maximal Timelike Geodesics in Static Spherically Symmetric Spacetimes: Radial Geodesics in Static Spacetimes and Arbitrary Geodesic Curves in Ultrastatic Spacetimes

This work deals with intersection points: conjugate points and cut points, of timelike geodesics emanating from a common initial point in special spacetimes. The paper contains three results. First, it is shown that radial timelike geodesics in static spherically symmetric spacetimes are globally maximal (have no cut points) in adequate domains. Second, in one of ultrastatic spherically symmetric spacetimes, Morris--Thorne wormhole, it is found which geodesics have cut points (and these must coincide with conjugate points) and which ones are globally maximal on their entire segments. This result, concerning all timelike geodesics of the wormhole, is the core of the work. The third outcome deals with the astonishing feature of all ultrastatic spacetimes: they provide a coordinate system which faithfully imitates the dynamical properties of the inertial reference frame. We precisely formulate these similarities.