Dimensional Wormhole Research Articles

Complexity and Multi-boundary Wormholes in 2 + 1 dimensions

Three dimensional wormholes are global solutions of Einstein-Hilbert action. These space-times which are quotients of a part of global AdS3 have multiple asymptotic regions, each with conformal boundary S1 × ℝ, and separated from each other by horizons. Each outer region is isometric to BTZ black hole, and behind the horizons, there is a complicated topology. The main virtue of these geometries is that they are dual to known CFT states. In this paper, we evaluate the full time dependence of holographic complexity for the simplest case of 2 + 1 dimensional Lorentzian wormhole spacetime, which has three asymptotic AdS boundaries, using the “complexity equals volume” (CV) conjecture. We conclude that the growth of complexity is non-linear and saturates at late times.

One dimensional wormhole corrosion in metals

Corrosion is a ubiquitous failure mode of materials. Often, the progression of localized corrosion is accompanied by the evolution of porosity in materials previously reported to be either three-dimensional or two-dimensional. However, using new tools and analysis techniques, we have realized that a more localized form of corrosion, which we call 1D wormhole corrosion, has previously been miscategorized in some situations. Using electron tomography, we show multiple examples of this 1D and percolating morphology. To understand the origin of this mechanism in a Ni-Cr alloy corroded by molten salt, we combined energy-filtered four-dimensional scanning transmission electron microscopy and ab initio density functional theory calculations to develop a vacancy mapping method with nanometer-resolution, identifying a remarkably high vacancy concentration in the diffusion-induced grain boundary migration zone, up to 100 times the equilibrium value at the melting point. Deciphering the origins of 1D corrosion is an important step towards designing structural materials with enhanced corrosion resistance.

Fluid accretion upon higher-dimensional wormhole and black hole for parameterized deceleration parameter

In this work, we study some parameterizations of the deceleration parameter and investigate the accretion of the fluid in these parameterized models upon the higher-dimensional black hole (BH) and wormholes. For the undergoing analysis, [Formula: see text]-dimensional wormhole (proposed by Morris and Thorne) and Schwarzschild BH were chosen in the backdrop of higher-dimensional Friedmann–Robertson–Walker (FRW) space-time. For these parameterized models, we analyze the change of masses of BH and wormhole in different dimensions.

Scattering of charged fermion to two-dimensional wormhole with constant axial magnetic flux

Scattering of charged fermion with (1+2)-dimensional wormhole in the presence of constant axial magnetic flux is explored. By extending the class of fermionic solutions of the Dirac equation in the curved space of wormhole surface to include normal modes with real energy and momentum, we found a quantum selection rule for the scattering of fermion waves to the wormhole. The newly found momentum–angular momentum relation implies that only fermion with the quantized momentum k=m'/asqrt{q} can be transmitted through the hole. The allowed momentum is proportional to an effective angular momentum quantum number m' and inversely proportional to the radius of the throat of the wormhole a. Flux dependence of the effective angular momentum quantum number permits us to select fermions that can pass through according to their momenta. A conservation law is also naturally enforced in terms of the unitarity condition among the incident, reflected, and transmitted waves. The scattering involving quasinormal modes (QNMs) of fermionic states in the wormhole is subsequently explored. It is found that the transmitted waves through the wormhole for all scenarios involving QNMs are mostly suppressed and decaying in time. In the case of QNMs scattering, the unitarity condition is violated but a more generic relation of the scattering coefficients is established. When the magnetic flux phi =mhc/e, i.e., quantized in units of the magnetic flux quantum hc/e, the fermion will tunnel through the wormhole with zero reflection.

The minimum deformation retract on the wormhole spacetime

In this paper, we investigate the topology of a wormhole from the viewpoint of the theory of retracting and var-folding. We deduce the equatorial geodesics on the line element of the wormhole and discuss the minimum deformation retract related to this space. Using the Lagrangian equations we find that there is a type of minimum retraction of a wormhole with associated topology. We also extend the result to the [Formula: see text]-dimensional wormhole and show that the end limit of var-folding is 0-dimensional wormhole and obtain the relation between limit var-folding and limit retraction. We find a new application in geometric topology and astrophysics.

Stability of charged rotating (2 + 1)-dimensional wormholes

This paper investigates the effects of charge on linearized stability of rotating thin-shell wormholes (WHs) filled with a barotropic fluid. We use Visser cut and paste technique to construct thin-shell from charged rotating Bañados–Teitelboim–Zanelli (BTZ) black holes (BHs). The components of stress-energy tensor are evaluated through Israel thin-shell formalism. The angular momentum for both interior as well as exterior region at the WH throat remains the same but opposite in direction, i.e. thin-shell WH at the throat is counter-rotated. It is found that the geometrical structure of WHs is more stable for highly charged and fast rotating thin-shell. We conclude that the stability regions of charged rotating WHs are larger than the uncharged rotating WHs.

Rotating thin-shell wormholes with scalar field

In this paper, we construct (2 + 1)-dimensional thin-shell wormholes from rotating Bañados–Teitelboim–Zanelli black hole and discuss their stability with the influence of scalar field at thin-shell. We apply Israel thin-shell formalism to evaluate surface stresses and study the behavior of energy conditions. We also study attractive and repulsive characteristics of the respective wormhole configurations according to the direction of radial acceleration. The linearized stability of rotating thin-shell wormholes is analyzed by assuming three different scalar field models at thin-shell. It is found that the increasing rate of angular momentum appears as an effective ingredient for stable wormholes while electric charge does not provide significant results in this regard. We conclude that less massive scalar field yields more stable 3D wormhole solutions.

Charged fermion in (1+2)-dimensional wormhole with axial magnetic field

We investigate the effects of magnetic field on a charged fermion in a (1+2)-dimensional wormhole. Applying external magnetic field along the axis direction of the wormhole, the Dirac equation is set up and analytically solved in two scenarios, constant magnetic flux and constant magnetic field through the throat of the wormhole. For the constant magnetic flux scenario, the system can be solved analytically and exact solutions are found. For the constant magnetic field scenario, with the short wormhole approximation, the quantized energies and eigenstates are obtained. The system exhibits both the spin-orbit coupling and the Landau quantization for the stationary states in both scenarios. The intrinsic curvature of the surface induces the spin-orbit and spin-magnetic Landau couplings that generate imaginary energy. Imaginary energy can be interpreted as the energy dissipation and instability of the states. Generically, the states of charged fermion in wormhole are quasinormal modes (QNMs) that could be unstable for positive imaginary frequencies and decaying for negative imaginary ones. For the constant flux scenario, the fermions in the wormhole can behave like bosons and have arbitrary statistics depending on the flux. We also discuss the implications of our results in the graphene wormholesystem.

(2+1)-dimensional wormhole from a doublet of scalar fields

We present a class of exact solutions in the framework of $(2+1)$-dimensional Einstein gravity coupled minimally to a doublet of scalar fields. Our solution can be interpreted upon the tuning of parameters as an asymptotically flat wormhole as well as a particle model in $2+1$ dimensions.

Lewis acidic ZrTUD-1 as catalyst for tert-butylation of phenol

A series of TUD-1 structures incorporated with Zr4+ for creating Lewis acidity were prepared by employing tetraethylene glycol (TEG) as a simple organic templating agent. These materials have varying nSi/nZr ratios and are shown to be disordered mesopores with narrow pore size distribution and a specific surface area of 600m2/g. Three dimensional wormhole like pores with Zr4+ in tetrahedral coordination was confirmed by HRTEM and diffuse reflectance UV–vis, XPS studies, respectively. The moderate Lewis acidity of ZrTUD-1 is shown to be a promising catalyst for gas phase tert-butylation of phenol.

Phantom Wormholes in (2+1)-Dimensions

In this paper, we have constructed a (2+1)-dimensional wormhole using inhomogeneous and anisotropic distribution of phantom energy. We have determined the exact form of the equation of state of phantom energy that supports the wormhole structure. Interestingly, this equation of state is linear but variable one and is dependent only on the radial parameter of the model.

Expanding (n+1)-dimensional wormhole solutions in Brans-Dicke cosmology

We have obtained two classes of $(n+1)$-dimensional wormhole solutions using a traceless energy-momentum tensor in Brans-Dicke theory of gravity. The first class contains wormhole solutions in an open geometry while the second contains wormhole solutions in both open and closed universes. In addition to wormhole geometries, naked singularities and maximally symmetric spacetime also appear among the solutions as special cases. We have also considered the travesibility of the wormhole solutions and have shown that they are indeed traverseable. Finally, we have discussed the energy-momentum tensor which supports this geometry and have checked for the energy conditions. We have found that wormhole solutions in the first class of solutions violate weak energy condition (WEC). In the second class, the wormhole geometries in a closed universe do violate WEC, but in an open universe with suitable choice of constants the supporting matter energy-momentum tensor can satisfy WEC. However, even in this case the full effective energy-momentum tensor including the scalar field and the matter energy-momentum tensor still violates the WEC.

Non-existence of static, spherically symmetric and stationary, axisymmetric traversable wormholes coupled to nonlinear electrodynamics

In this work we explore the possible existence of static, spherically symmetric and stationary, axisymmetric traversable wormholes coupled to nonlinear electrodynamics. Considering static and spherically symmetric (2 + 1)- and (3 + 1)-dimensional wormhole spacetimes, we verify the presence of an event horizon and the non-violation of the null energy condition at the throat. For the former spacetime, the principle of finiteness is imposed, in order to obtain regular physical fields at the throat. Next, we analyse the (2 + 1)-dimensional stationary and axisymmetric wormhole, and also verify the presence of an event horizon, rendering the geometry non-traversable. Relative to the (3 + 1)-dimensional stationary and axisymmetric wormhole geometry, we find that the field equations impose specific conditions that are incompatible with the properties of wormholes. Thus, we prove the non-existence of the general class of traversable wormhole solutions, outlined above, within the context of nonlinear electrodynamics.

Evolving wormhole geometries within nonlinear electrodynamics

In this work, we explore the possibility of evolving (2 + 1) and (3 + 1)-dimensional wormhole spacetimes, conformally related to the respective static geometries, within the context of nonlinear electrodynamics. For the (3 + 1)-dimensional spacetime, it is found that the Einstein field equation imposes a contracting wormhole solution and the obedience of the weak energy condition. Nevertheless, in the presence of an electric field, the latter presents a singularity at the throat; however, for a pure magnetic field the solution is regular. For the (2 + 1)-dimensional case, it is also found that the physical fields are singular at the throat. Thus, taking into account the principle of finiteness, which states that a satisfactory theory should avoid physical quantities becoming infinite, one may rule out evolving (3 + 1)-dimensional wormhole solutions, in the presence of an electric field, and the (2 + 1)-dimensional case coupled to nonlinear electrodynamics.

Higher dimensional wormhole geometries with compact dimensions

This paper studies wormhole solutions to Einstein gravity with an arbitrary number of time dependent compact dimensions and a matter-vacuum boundary. A new gauge is utilized which is particularly suited for studies of the wormhole throat. The solutions possess arbitrary functions which allow for the description of infinitely many wormhole systems of this type and, at the stellar boundary, the matter field is smoothly joined to vacuum. It turns out that the classical vacuum structure differs considerably from the four-dimensional theory and is, therefore, studied in detail. The presence of the vacuum-matter boundary and extra dimensions places interesting restrictions on the wormhole. For example, in the static case, the radial size of a weak energy condition (WEC) respecting throat is restricted by the extra dimensions. There is a critical dimension, D=5, where this restriction is eliminated. In the time dependent case, one cannot respect the WEC at the throat as the time dependence actually tends the solution towards WEC violation. This differs considerably from the static case and the four-dimensional case.

Energy computation in wormhole background with the Wheeler-DeWitt operators

We investigate the possibility of computing energy by means of operators associated to the Wheeler-DeWitt equation. By choosing three dimensional wormholes as a framework, we apply this calculation to black hole pair creation. We compare our results with recent results in the literature.