Static Wormhole Research Articles

Complexity factor parameterization for traversable wormholes

It is known that static traversable wormholes in Einstein gravity are supported by matter that violates null energy conditions (NEC). Essentially, such wormholes will be characterized by a central throat with anisotropic matter lining the throat that violates NEC. This, in turn, provides viable geometry for the wormhole to sustain. In 2018, Herrera [Phys. Rev. D 97, 044010 (2018)] introduced a new classification for spherically symmetric bodies called “complexity factor.” It was proposed that a spherically symmetric non-trivial geometry can be classified as complex or non-complex based on the nature of the inhomogeneity and anisotropy of the stress–energy tensors with only homogeneous and isotropic matter distribution leading to null complexity. Mathematically, there was also another way of obtaining zero complexity geometry. In this context, since static traversable wormholes, by default, are characterized by anisotropic and inhomogeneous matter stress tensors, the question we answer is whether it is possible to obtain zero complexity class of wormholes supported by exotic matter.

Polar modes and isospectrality of Ellis-Bronnikov wormholes

We consider polar perturbations of static Ellis-Bronnikov wormholes and derive the coupled set of perturbation equations for the gravitational and the scalar field. For massless wormholes the perturbations decouple, and we obtain two identical master equations for the scalar and gravitational modes, which moreover agree with the master equation for the axial modes. Consequently there is isospectrality with threefold degenerate modes. For a finite mass of the background wormhole solutions, the equations are coupled. We then obtain two distinct branches of polar quasinormal modes for a given multipole number l, associated with the presence of the two types of fields. We calculate the quasi-normal mode frequencies and decay rates for the branches with l=2, 3 and 4. For a given l the real frequencies of the two branchesget the closer, the higher the multipole number gets.

Lorentzian wormholes in an emergent universe

A non-singular emergent universe (EU) scenario within the realm of standard Relativistic physics requires a generalization of the equation of state (EoS) connecting the pressure and energy density. This generalized EoS is capable of describing a composition of exotic matter, dark energy and cosmological dust matter. Since the EU scenario is known to violate the null energy condition (NEC), we investigate the possibility of presence of static, spherically symmetric and traversable Lorentzian wormholes in an EU. The obtained shape function is found to satisfy the criteria for wormhole formation, besides the violation of the NEC at the wormhole throat and ensuring traversability such that tidal forces are within desirable limits. Also, the wormhole is found to be stable through linear stability analysis. Most importantly, the numerical value of the EU parameter B as estimated by our wormhole model is in agreement with and lies within the range of values as constrained by observational data in a cosmological context. Also, the negative sign of the second EU parameter A as obtained from our wormhole model is in agreement with the one required for describing an EU, which further indicates on the existence of such wormholes in an EU without accounting for any additional exotic matter field or any modification to the gravitational sector.

Traversable wormhole solutions admitting Karmarkar condition in f(R, T) theory

In this paper, we evaluate traversable wormhole solutions through Karmarkar condition in f(R, T) theory, where T is the trace of the energy-momentum tensor and R represents the Ricci scalar. We develop a wormhole shape function for the static traversable wormhole geometry by using the embedding class-I technique. The resulting shape function is used to construct wormhole geometry that fulfills all the necessary conditions and joins the two asymptotically flat regions of the spacetime. We investigate the existence of viable traversable wormhole solutions for anisotropic matter configuration and examine the stable state of these solutions for different f(R, T) gravity models. We analyze the graphical behavior of null energy bound to examine the presence of physically viable wormhole geometry. It is found that viable and stable traversable wormhole solutions exist in this modified theory of gravity.

Potentials vs geometry, revisited

We revisit an old subject to discuss relationships between the dynamics for particles subjected to potentials and the dynamics for particles moving freely on background geometries, in the context of non-relativistic quantum mechanics. In particular, we illustrate how selected geometries can be used to regularize singular potentials. We also compute scattering amplitudes for quanta incident on a static non-relativistic wormhole.

Probing the existence of the ZTF Casimir wormholes in the framework of [formula omitted] gravity

For the spherically symmetric static traversable wormholes, supported by the Casimir energy in f(R)=R+αR2 Quadratic, f(R)=f0Rn power-law Modified Gravity (MOG) theories we investigate energy conditions and dynamical stability of the wormhole solutions. Especially, we study Zero Tidal Forces (ZTF) Casimir WH's with anisotropic fluid located at the throat. By using the Casimir energy density and modified Einstein Field Equations (EFE's) we derived suitable shape functions for each modified gravity of our consideration. The stability of Casimir traversable wormholes in different modified gravity theories is also analyzed in our paper with a modified Tolman-Oppenheimer-Voklov (MTOV) equation. Besides, we have numerically solved MTOV and derived hydrodynamical, anisotropic and extra forces, that is present due to the non-conserved stress-energy tensor. Moreover, other fundamental quantities, such as Volume Integral Quantifier and total gravitational energy were derived

Existence of wormholes in f(𝒢) gravity using symmetries

The current study examines the geometry of static wormholes with anisotropic matter distribution in the context of modified [Formula: see text] gravity. We consider the well-known Noether and conformal symmetries, which help in investigating wormholes in [Formula: see text] gravity. For this purpose, we develop symmetry generators associated with conserved quantities by taking into consideration the [Formula: see text] gravity model. Moreover, we use the conservation relationship gained from the classical Noether method and conformal Killing symmetries to develop the metric potential. These symmetries provide a strong mathematical background to investigate wormhole solutions by incorporating some suitable initial conditions. The obtained conserved quantity performs a significant role in defining the essential physical characteristics of the shape-function and energy conditions. Further, we also describe the stability of obtained wormholes solutions by employing the equilibrium condition in modified [Formula: see text] gravity. It is observed from graphical representation of obtained wormhole solutions that Noether and conformal Killing symmetries provide the results with physically accepted patterns.

Characterization of Wormhole Growth and Propagation Dynamics During Cold Heavy Oil Production with Sand (CHOPS) Processes by Integrating Rate Transient Analysis and a Pressure-Gradient-Based Sand Failure Criterion

Summary In this work, theoretical models have been formulated, validated, and applied to characterize the dynamic wormhole growth and propagation dynamics during cold heavy oil production with sand (CHOPS) processes by integrating rate transient analysis (RTA) and a pressure-gradient-based (PGB) sand failure criterion. More specifically, a coupling fluid-solid flow model is proposed by incorporating the recently proposed PGB sand failure criterion with sand production. Then, the source function method is applied to solve the fluid flow problem in the matrix subsystem by considering each generated wormhole segment as a sink source, while the finite difference method is applied to solve the fluid-sand flow problem in the wormhole subsystem. The sand failing at each segment is induced and propagated once the PGB sand failure criterion has been reached. Furthermore, transient-rate-type curves are generated to determine the dynamic wormhole network conditioned to the measured fluids and sand production profiles. Also, effects of the PGB sand failure criterion and reservoir properties on the transient rate behavior for CHOPS wells can be examined and analyzed. A gradual increase in the production rate profile occurs at the early times due to the wormhole growth and propagation. The wormhole network can be dynamically characterized by matching both the sand production rate and transient fluid production rate. The former is found to be greatly affected by the breakdown pressure gradient, while the effective wormhole coverage and intensity dominate the latter. Once the transient rate responses for both static and dynamic wormhole networks are validated with numerical simulation, the newly proposed method has been extended to field applications under various constraints, demonstrating that the fluid and sand production data of CHOPS wells can be integrated to accurately characterize the dynamic wormhole network within a unified, consistent, and efficient framework.

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.

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.

Wave optics and weak gravitational lensing of lights from spherically symmetric static scalar vector tensor Brans Dicke wormholes

This paper has three parts. In first step we use modified scalar tensor vector Brans Dicke gravity \cite{GH0} to obtain metric solution of a spherically symmetric static black hole via perturbation method which asymptotically behaves as modified Schwarzschild de Sitter black hole in weak field limits. Corrections on the line element with respect to the point mass Schwarzschild de Sitter black hole are two parts: power law function for black hole mass instead of point mass and additional logarithmic metric potential which they are produced from effects of interacting timelike dynamical vector fields. Second part of the paper is dedicated to review Fresnel-Kirchhoff diffraction theory for massless scalar field instead of the vector electromagnetic waves. In third part of the work we consider the obtained black hole metric to be lens and we study weak gravitational lensing of moving light originated from point star. Production of stationary images is investigated via both interference of waves and geometric optics approaches. At last we compare results of these approaches and give some outlooks.

Revisiting the evolving Lorentzian wormhole: a general perspective

Wormholes can be described as geometrical structures in space and time that can serve as connection between distant regions of the universe. Mathematically, general wormholes can be defined both on stationary as well as on dynamic line elements. However, general relativistic and evolving Lorentzian wormholes are less studied than their static wormhole counterpart. Accordingly, in this work we shall focus on some evolving wormhole geometries. Starting from a general class of spherically symmetric line element supporting wormhole geometries, we shall use the Einstein's field equations to develop viable astatic wormhole solutions. We will also discuss various evolving wormhole solutions together with their physical significance, properties and throat energy conditions. We claim that the method discussed in this work shall be applicable for developing wormhole solutions corresponding to any general Lorentzian wormhole metric.

How to make traversable wormholes: eternal AdS4 wormholes from coupled CFT\u2019s

We construct an eternal traversable wormhole connecting two asymptotically AdS4 regions. The wormhole is dual to the ground state of a system of two identical holographic CFT’s coupled via a single low-dimension operator. The coupling between the two CFT’s leads to negative null energy in the bulk, which supports a static traversable wormhole. As the ground state of a simple Hamiltonian, it may be possible to make these wormholes in the lab or on a quantum computer.

A Note on “Traversable Wormholes in Einstein–Dirac–Maxwell Theory”

In their Letter [Phys. Rev. Lett. 126, 101102 (2021); arXiv: 2010.07317], J.L. Bl\'azquez-Salcedo, C. Knoll and E. Radu have constructed a very interesting class of wormhole solutions in GR, supported by a pair of classical charged spinor fields obeying the Dirac equation. The main new feature of these solutions is that such Dirac spinor fields can possess exotic properties, necessary for the existence of static wormhole configurations in GR. The present note contains a few remarks clarifying some points concerning this approach.

Wormhole as a waveguide for non-relativistic quantum particles

We consider a static wormhole as a waveguide and determine the conditions for full transmission through the wormhole waveguide for a quantum particle satisfying Schrodinger equation. We find that the waveguide is transparent when the angular momentum L of the quantum particle is 0 and for when the de Broglie wavelength of the quantum particle is a multiple depending on the inverse of the angular momentum times the throat radius of the wormhole.

On the existence and stability of traversable wormhole solutions in modified theories of gravity

We study Morris–Thorne static traversable wormhole solutions in different modified theories of gravity. We focus our study on the quadratic gravity f({mathscr {R}}) = {mathscr {R}}+a{mathscr {R}}^2, power-law f({mathscr {R}}) = f_0{mathscr {R}}^n, log-corrected f({mathscr {R}})={mathscr {R}}+alpha {mathscr {R}}^2+beta {mathscr {R}}^2ln beta {mathscr {R}} theories, and finally on the exponential hybrid metric-Palatini gravity f(mathscr {hat{R}})=zeta bigg (1+e^{-frac{hat{{mathscr {R}}}}{varPhi }}bigg ). Wormhole fluid near the throat is adopted to be anisotropic, and redshift factor to have a constant value. We solve numerically the Einstein field equations and we derive the suitable shape function for each MOG of our consideration by applying the equation of state p_t=omega rho . Furthermore, we investigate the null energy condition, the weak energy condition, and the strong energy condition with the suitable shape function b(r). The stability of Morris–Thorne traversable wormholes in different modified gravity theories is also analyzed in our paper with a modified Tolman–Oppenheimer–Voklov equation. Besides, we have derived general formulas for the extra force that is present in MTOV due to the non-conserved stress-energy tensor.

Wormhole geometry from gravitational collapse

We discuss a proposal on how gravitational collapse of a null energy condition violating spherically symmetric fluid distribution can avoid the formation of a zero proper volume singularity and eventually lead to a Lorentzian wormhole geometry. Our idea is illustrated using a time-evolving wormhole spacetime in which we show how a collapsing sphere may never reach a zero proper volume end state. The nature of geodesic congruences in such spacetimes is considered and analyzed. Our construction is inspired from a recently proposed static wormhole geometry, the multiparameter Simpson-Visser line element, which is known to unite wormholes and black holes (regular and singular) in a single framework.

Thermodynamics of traversable wormholes in f(R,T) gravity

In this paper, we discuss thermodynamics for spherically symmetric and static traversable wormholes which include Morris–Thorne wormholes and charged wormholes in the background of [Formula: see text] gravity. The local coordinates have been used to find trapping horizons of these objects and generalized surface gravity has been worked out on the trapping horizons. The expression for the unified first law has also been derived from the gradient of Misner–Sharp energy with the help of gravitational field equations and from this law the first law of wormhole dynamics has been obtained. We have done this analysis for the simplest case of [Formula: see text] gravity where [Formula: see text], [Formula: see text] and [Formula: see text] being the traces of the Ricci and stress–energy tensors. Also, we have extended these thermodynamic results to non-minimal curvature-matter coupling.

Thermodynamics of dynamical wormholes

We study thermodynamics of dynamical traversable wormholes. The surface gravity is evaluated on the trapping horizon and the unified first law of thermodynamics is set up. The thermodynamic stability of these wormholes has been investigated. We have also extended these results to charged dynamical wormholes. Our results generalize those that exist for static Morris-Thorne wormholes.

Viable wormhole solutions in energy–momentum squared gravity

This paper investigates static wormhole solutions through Noether symmetry approach in the context of energy–momentum squared gravity. This newly developed proposal resolves the singularity of big bang and yields feasible cosmological results in the early times. We consider the particular model of this theory to establish symmetry generators and corresponding conserved quantities. For constant and variable red-shift functions, we examine the presence of viable traversable wormhole solutions for both dust and non-dust matter distributions and analyze the stable state of these solutions. We investigate the graphical interpretation of null and weak energy bounds for normal and effective energy–momentum tensors to examine the presence of physically viable wormhole geometry. It is found that realistic traversable and stable wormhole solutions are obtained for a particular model of this gravity.