Wormhole Throat Research Articles

Generalized Ellis–Bronnikov wormholes in asymptotically safe gravity

In this paper we study a class of wormhole solutions called generalized Ellis–Bronnikov wormholes in the context of asymptotically safe gravity (ASG). These solutions are characterized by two parameters: an even number n and the wormhole throat radius rt. The particular case n=2 recovers the usual Ellis–Bronnikov spacetime, which has already been addressed in the literature. We analyzed the nature of matter in the wormhole’s throat, and in nearby regions, of these generalized solutions with n>2, using three curvature scalars in the ASG approach, namely, the Ricci scalar, squared Ricci and the Kretschmann scalar. We have shown that the ASG leads to corrections in the matter at the wormhole’s throat only for the n=4 case. For the squared Ricci and the Kretschmann we find that exotic matter is always necessary, as previously found for the usual Ellis–Bronnikov. However, for the Ricci scalar case, we found that ordinary matter is allowed at the throat. Therefore, the generalized Ellis–Bronnikov wormhole provides to the possibility of having ordinary matter at the throat in the context of asymptotically safe gravity.

Matter traveling through a wormhole

We revisit the numerical evolution of Ellis-Bronnikov-Morris-Thorne wormholes, which are constructed with a massless real ghost scalar field. For our simulations, we have developed a new code based on the standard $3+1$ foliation of spacetime. We confirm that, for the massless symmetric wormhole, a pulse of regular scalar field causes the wormhole throat to collapse and form an apparent horizon, while a pulse of ghost scalar field can cause the wormhole throat to expand. As a new result, we show that it is possible for a pulse of regular matter to travel through the wormhole and then to send a light signal back before the wormhole collapses. We also evolve pulses of matter traveling through massive asymmetric wormholes, which has not previously been simulated.

Scalar Particles around a Rindler–Schwarzschild Wormhole

In this paper, we study quantum relativistic features of a scalar field around the Rindler–Schwarzschild wormhole. First, we introduce this new class of spacetime, investigating some energy conditions and verifying their violation in a region nearby the wormhole throat, which means that the object must have an exotic energy in order to prevent its collapse. Then, we study the behavior of the massless scalar field in this spacetime and compute the effective potential by means of tortoise coordinates. We show that such a potential is attractive close to the throat and that it is traversable via quantum tunneling by massive particles with sufficiently low energies. The solution of the Klein–Gordon equation is obtained subsequently, showing that the energy spectrum of the field is subject to a constraint, which induces a decreasing oscillatory behavior. By imposing Dirichlet boundary conditions on a spherical shell in the neighborhood of the throat we can determine the particle energy levels, and we use this spectrum to calculate the quantum revival of the eigenstates. Finally, we compute the Casimir energy associated with the massless scalar field at zero temperature. We perform this calculation by means of the sum of the modes method. The zero-point energy is regularized using the Epstein–Hurwitz zeta-function. We also obtain an analytical expression for the Casimir force acting on the shell.

Further considerations about the traversability of thin-shell wormholes

Traversability in relation with tides in thin-shell wormholes is revisited to investigate the possibility of improving recently noted restrictive conditions for a safe travel across a wormhole throat. We consider wormholes mathematically constructed starting from background geometries which are solutions of scalar–tensor theories as dilaton gravity and Brans–Dicke gravity. The advantages of working within such frameworks are studied by examining the dependence of the extrinsic curvature and tides at the throat with the parameters determining the departure from pure relativity; the associated behaviour of tides in the smooth regions of the geometries is also analyzed. Other related but different approaches within pure relativity are discussed in the appendices.

On a Class of Harko-Kovacs-Lobo Wormholes

The Harko, Kovács, and Lobo wormhole (HKLWH) metric contains two free parameters: one is the wormhole throat r0, and the other is a dimensionless deviation parameter γ with values 0<γ<1, the latter ensuring the needed violation of the null energy condition at the throat. In this paper, we study the energetics of the HKLWH and the influence of γ on the tidal forces in the Lorentz-boosted frame. Finally, we apply a new concept, namely, the probabilistic identity of the object observed by different external observers in terms of the Fresnel coefficients derived by Tangherlini. The intriguing result is that observations can differ depending on the location of the observer, i.e., there is a nonzero probability that the HKLWH will be identified as a black hole even when γ≠0.

Validation of energy conditions in traversable wormhole for GBD modified theory

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: [Formula: see text], 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.

Dynamics and stability of Bardeen-de Sitter thin shell wormholes

A dynamical equation of thin-shell wormhole joining two identical copies of non-singular Bardeen-de Sitter black hole spacetime through the cut and paste techniques is constructed. The stability of the Bardeen-de Sitter wormhole, as the static solution of linear perturbation at the wormhole throat and a variable modified generalized Chaplygin gas equation of state, is analyzed.The existence of stability configurations depends on the particular values of different parameters involved in the equation of state as well as the space-time metric performed. The existence of Bardeen-de Sitter parameters and the equation of state parameters to enlarge the stability regions may be obtained.

Phantom scalar field counterpart to Curzon–Chazy spacetime

We derive and analyze phantom scalar field counterpart to Curzon–Chazy spacetime. Such solution contains a wormhole throat while the region inside the throat behaves like a one-directional time machine. We describe its conformal structure and non-scalar singularity hidden inside the wormhole. We examine the results provided by different definitions of mass of the spacetime to understand their value in the presence of phantom matter. The electromagnetic generalization of this spacetime is as well briefly considered.

Twin Peak Quasi‐Periodic Oscillations and Stability via Thin‐Shell Formalism of Traversable Wormholes in Symmetric Teleparallel Gravity

AbstractThis article explores the wormhole geometry in the background of symmetric teleparallel gravity or gravity, where is the non‐metricity term, and definite subject for the gravitational interaction. All the energy conditions are investigated for two different generic shape functions. The presence of exotic matter is confirmed due to the violation of the energy conditions. The epicyclic orbits of test particles around wormhole throat for the considered models are discussed. Twin peak Quasi‐periodic oscillations are calculated and presented with the required behavior. We also explore the physical characteristics and stable configuration of thin‐shell developed from the matching of inner obtained solution of wormhole geometry and outer black hole solution in gravity. The stability of shell is discussed by using the speed of sound parameter for both choices of shape functions, i.e., and . It is found that the position of event horizon does not change for different values of the physical parameter for the choice of while it changes for . We explore the proper length, shell energy and entropy of the developed structure for different values of physical parameters.

Traversable wormholes with charge and non-commutative geometry in the [formula omitted] gravity

We consider modified symmetric teleparallel gravity (STG), in which gravitational Lagrangian is given by the arbitrary function of non-metricity scalar Q to study static and spherically symmetric charged traversable wormhole solutions with non-commutative background geometry. The matter source at the wormhole throat is acknowledged to be anisotropic, and the redshift function has a constant value (thus, our wormhole solution is non-tidal). We study the obtained field equations with the two functional forms of f(Q) STG models, such as linear f(Q)=αQ+β and non-linear f(Q)=Q+mQn models under Gaussian and Lorentzian distributions. Our analysis found the exact wormhole solutions for the linear STG model only. Also, for the non-linear model, we derived numerically suitable forms of wormhole shape functions directly from the modified Einstein Field Equations (EFEs). Besides, we probed these models via Null, Dominant, and Strong energy conditions with respect to free Modified gravity (MOG) parameters α, β, m, and n. We also used Tolman–Oppenheimer–Vokloff (TOV) equation to investigate the stability of wormhole anisotropic matter in considered MOG. Finally, we plot the equation of state.

Charged traversable wormholes supported by Casimir energy with and without GUP corrections

In this paper, we investigate new exact and analytic solutions of the Einstein–Maxwell field equations describing Casimir wormholes with and without the effect of the Generalized Uncertainty Principle (GUP). We consider a specific type of the GUP relations and study three specific models of the redshift function along with two different EoS of state given by pr(r)=ωr(r)ρ(r) and pt(r)=ωt(r)pr(r). Here we obtain a class of asymptotically flat Casimir wormhole solutions with and without GUP corrections under the effect of electric charge. Furthermore we check the null, weak, strong and dominant energy conditions at the wormhole throat of radius r0, and show at the wormhole throat that the classical energy conditions are violated by some arbitrary small quantity. We also examine the wormhole geometry with semi-classical corrections by using embedding diagrams. We use the volume integral quantifier to quantify the amount of the exotic matter near the wormhole throat. Additionally, we investigate exotic fluid near WH throat using the so-called exoticity parameter and discuss the speed of sound.

F(R)$f(R)$ Wormholes Embedded in a Pseudo–Euclidean Space E5

AbstractThis work is devoted to the study of analytic wormhole solutions within the framework of gravity theory. To check the possibility of having wormhole structures satisfying energy conditions, by means of the class I approach the pair describing the wormhole geometry has been obtained. Then, in conjunction with a remarkably gravity model, the satisfaction of the null and weak energy conditions at the wormhole throat and its neighborhood is investigated. To do so, some constant parameters have been bounded restricting the space parameter. In this concern, the gravity model and its derivatives are playing a major role, specially in considering the violation of the non–existence theorem. Furthermore, the shape function should be bounded from above by the Gronwall–Bellman shape function, where the red–shift function plays a relevant role. By analyzing the main properties at the spatial stations and tidal accelerations at the wormhole throat, possibilities and conditions for human travel are explored.

Analogue Metric in a Black-Bounce Background

The conventional approach of embedding an effective acoustic metric for sound motion in a background flat Minkowski space-time has recently been extended to incorporate more general curved background metrics, which might contain a black hole. Though the observational aspects of these kinds of acoustics horizons, including the sonic shadow structure and quasi normal modes, have received significant attention in the literature, there is room left for discussions about embedding more general classes of curved background space-times without optical horizons. Here, we propose and study a new class of acoustic metrics that is embedded in a black-bounce space-time, thereby giving a suitable tuneable system to understand possible observational effects of the presence or absence of acoustic horizons. After showing that the metric can represent five types of different effective backgrounds for sound motion, including a novel “acoustic wormhole–optical wormhole” branch, we discuss how the distinctive features of sonic shadows can appear even in the absence of any acoustic horizon due to the wormhole throat present in the acoustic metric.

Simple traversable wormholes violating energy conditions only near the Planck scale

We present a static and axisymmetric traversable wormhole spacetime with vanishing Arnowitt-Deser-Misner (ADM) mass which is characterized by a length parameter l and a deformation parameter a and reduces to the massless Kerr vacuum wormhole as l → 0. The spacetime is analytic everywhere and regularizes a ring-like conical singularity of the massless Kerr wormhole by virtue of a localized exotic matter which violates the standard energy conditions only near the wormhole throat. In the spherically symmetric case (a = 0), the areal radius of the wormhole throat is exactly l and all the standard energy conditions are respected outside the proper radial distance approximately 1.60l from the throat. While the curvature at the throat is beyond the Planck scale if l is identical to the Planck length l p, our wormhole may be a semi-classical model for l ≃ 10l p. With l = 10l p, the total amount of the negative energy supporting this wormhole is only E ≃ −26.5m p c 2, which is the rest mass energy of about −5.77 × 10−4 g. It is shown that the geodesic behavior on the equatorial plane does not qualitatively change by the localization of an exotic matter.

Probing the Ellis-Bronnikov wormhole geometry with a scalar field: Clouds, waves and Q-balls

The Ellis-Bronnikov solution provides a simple toy model for the study of various aspects of wormhole physics. In this work we solve the Klein-Gordon equation in this background and find an exact solution in terms of Heun's function. This may describe ‘scalar clouds’ (i.e. localized, particle-like configuration) or scalar waves. However, in the former case, the radial derivative of the scalar field is discontinuous at the wormhole's throat (except for the spherical case). This pathology is absent for a suitable scalar field self-interaction, and we provide evidence for the existence of spherically symmetric and spinning Q-balls in a Ellis-Bronnikov wormhole background.

Smeared mass source wormholes in modified f(R) gravity with the Lorentzian density distribution function

Wormholes are speculative structures linking disparate spacetime points. Their geometry can be obtained by solving Einstein equations with tolerating the violation of null energy conditions (NEC). Recently, many researchers have studied different wormholes according to different criteria, and they achieved remarkable results. In this paper, we investigate a series of exact solutions of the static wormhole with smeared mass source geometry in modified [Formula: see text] gravity theories. In fact, we consider the Lorentzian density distribution which is coming from a particle-like source. To be more specific, the modified gravity models we consider here are some power laws. We compute resulting solutions according to the wormhole field equations. We also specify parameters such as the radial pressure and transverse pressure as well as various energy conditions such as NEC, weak energy conditions and strong energy conditions. Finally, by plotting some figures, in addition to identifying the wormhole throat, we describe the results of either the violation or the satisfaction of the energy conditions completely.

Wormholes in Poincarè gauge theory of gravity

In this work, we study static spherically symmetric solutions representing wormhole configurations in Poincarè gauge theory ( PGT ). The gravitational sector of the Lagrangian is chosen as a subclass of PGT Lagrangians for which the spin-[Formula: see text] is the only propagating torsion mode. The spacetime torsion in PGT has a dynamical nature even in the absence of intrinsic angular momentum (spin) of matter, hence torsion can play a principal role in the case of usual spin-less gravitating systems. We therefore consider a spin-less matter distribution with an anisotropic energy–momentum tensor ( EMT ) as the supporting source for wormhole structure to obtain a class of zero tidal force wormhole solutions. It is seen that the matter distribution obeys the physical reasonability conditions, i.e. the weak ( WEC ) and null ( NEC ) energy conditions either at the throat and throughout the spacetime. We further consider varying equations of state in radial and tangential directions via definitions [Formula: see text] and [Formula: see text] and investigate the behavior of state parameters at the throat of wormhole. We observe that our solutions allow for wormhole configurations without the need of exotic matter. Observational features of the wormhole solutions are also discussed utilizing gravitational lensing effects. It is found that the light deflection angle diverges at the throat (which indeed, effectively acts as a photon sphere) and can get zero and negative values depending on the model parameters.

Blázquez-Salcedo–Knoll–Radu wormholes are not solutions to the Einstein-Dirac-Maxwell equations

Recently, Bl\'azquez-Salcedo, Knoll, and Radu (BSKR) have given a class of static, spherically symmetric, traversable wormhole spacetimes with Dirac and Maxwell fields. The BSKR wormholes are obtained by joining a classical solution to the Einstein-Dirac-Maxwell (EDM) equations on the "up" side of the wormhole ($r \geq 0$) to a corresponding solution on the "down" side of the wormhole ($r \leq 0$). However, it can be seen that the BSKR metric fails to be $C^3$ on the wormhole throat at $r=0$. We prove that if the matching were done in such a way that the resulting spacetime metric, Dirac field, and Maxwell field composed a solution to the EDM equations in a neighborhood of $r=0$, then all of the fields would be smooth at $r=0$ in a suitable gauge. Thus, the BSKR wormholes cannot be solutions to the EDM equations. The failure of the BSKR wormholes to solve the EDM equations arises both from the failure of the Maxwell field to satisfy the required matching conditions (which implies the presence of an additional shell of charged matter at $r=0$) and, more significantly, from the failure of the Dirac field to satisfy required matching conditions (which implies the presence of a spurious source term for the Dirac field at $r=0$.

Magnetized Dusty Black Holes and Wormholes

We consider the generalized Tolman solution of general relativity, describing the evolution of a spherical dust cloud in the presence of an external electric or magnetic field. The solution contains three arbitrary functions f(R), F(R) and τ0(R), where R is a radial coordinate in the comoving reference frame. The solution splits into three branches corresponding to hyperbolic (f>0), parabolic (f=0) and elliptic (f<0) types of motion. In such models, we study the possible existence of wormhole throats defined as spheres of minimum radius at a fixed time instant, and prove the existence of throats in the elliptic branch under certain conditions imposed on the arbitrary functions. It is further shown that the normal to a throat is a timelike vector (except for the instant of maximum expansion, when this vector is null), hence a throat is in general located in a T-region of space-time. Thus, if such a dust cloud is placed between two empty (Reissner–Nordström or Schwarzschild) space-time regions, the whole configuration is a black hole rather than a wormhole. However, dust clouds with throats can be inscribed into closed isotropic cosmological models filled with dust to form wormholes which exist for a finite period of time and experience expansion and contraction together with the corresponding cosmology. Explicit examples and numerical estimates are presented. The possible traversability of wormhole-like evolving dust layers is established by a numerical study of radial null geodesics.

Infall time in the Eddington–Finkelstein metric, with application to Einstein–Rosen bridges

Eddington–Finkelstein metric is obtained from the Schwarzschild metric by a change of the time variable. It is well known that a test mass falling into a black hole does not reach the event horizon for any finite value of the Schwarzschild time variable [Formula: see text]. By contrast, we show that the event horizon is reached for a finite value of the Eddington–Finkelstein time variable [Formula: see text]. Then we study in Eddington–Finkelstein time the fate of a massive particle traversing an Einstein–Rosen bridge and obtain a different conclusion than recent proposals in the literature: we show that the particle reaches the wormhole throat for a finite value [Formula: see text] of the time marker [Formula: see text], and continues its trajectory across the throat for [Formula: see text]. Such a behavior does not make sense in Schwarzschild time since it would amount to continuing the trajectory of the particle “beyond the end of time.”