The problem of the electrostatics in conical wormholes is revisited, now improving the background geometries with asymptotical flatness. The electric self-force on a point charge placed at different regions in the spacetime of a conical thin-shell wormhole connecting flat outer submanifolds is obtained and compared with the results of previous works. The study is also carried out in terms of a previously introduced analogy in which the effect of the matter shells on the electric field is reproduced by non-gravitating layers of charge located on the boundary surfaces. Besides, a better insight on the physical effects of a non trivial topology is obtained by means of a further analysis of the electric fluxes across the wormhole throat and at both spatial infinities. It is found that the throat is traversed by a non-arbitrary and finite topological flux, proportional to the charge of the source, which is characteristic of the asymptotically flat cylindrical wormholes regardless of the details of the throat geometry.
We determine in closed form the electrostatic potential generated by a point charge at rest in a simple model of static spherically symmetric wormhole. From this, we deduce the electrostatic self-energy of this point charge.
This paper discusses traversable wormholes that differ slightly but significantly from those of the Morris-Thorne type under the assumption of cylindrical symmetry. The throat is a piecewise smooth cylindrical surface resulting in a shape function that is not differentiable at some value. It is proposed that the regular derivative be replaced by a one-sided derivative at this value. The resulting wormhole geometry satisfies the weak energy condition.
In this paper, we consider the stability of cylindrical wormholes during evolution of universe from inflation to late time acceleration epochs. We show that there are two types of cylindrical wormholes. The first type is produced at the corresponding point where k black F-strings are transited to BIon configuration. This wormhole transfers energy from extra dimensions into our universe, causes inflation, loses it's energy and vanishes. The second type of cylindrical wormhole is created by a tachyonic potential and causes a new phase of acceleration. We show that wormhole parameters grow faster…
It is shown that the existence of static, cylindrically symmetric wormholes does not require violation of the weak or null energy conditions near the throat, and cylindrically symmetric wormhole geometries can appear with less exotic sources than wormholes whose throats have a spherical topology. Examples of exact wormhole solutions are given with scalar, spinor and electromagnetic fields as sources, and these fields are not necessarily phantom. In particular, there are wormhole solutions for a massless, minimally coupled scalar field in the presence of a negative cosmological constant, and fo…
We prove the impossibility of cylindrical thin-shell wormholes supported by matter satisfying the energy conditions everywhere, under reasonable assumptions about the asymptotic behaviour of the - in general different - metrics at each side of the throat. In particular, we reproduce for singular sources previous results corresponding to flat and conical asymptotics, and extend them to a more general asymptotic behaviour. Besides, we establish necessary conditions for the possibility of non exotic cylindrical thin-shell wormholes.
The electrostatic potential generated by a point charge at rest in a simple static, spherically symmetric wormhole is given in the form of series of multipoles and in closed form. The general potential which is physically acceptable depends on a parameter due to the fact that the monopole solution is arbitrary. When the wormhole has Z2-symmetry, the potential is completely determined. The calculation of the electrostatic self-energy and of the self-force is performed in all cases considered.
We revisit the stability analysis of cylindrical thin shell wormholes which have been studied in literature so far. Our approach is more systematic and in parallel to the method which is used in spherically symmetric thin shell wormholes. The stability condition is summarized as the positivity of the second derivative of an effective potential at the equilibrium radius, i.e. $V^{\prime \prime}\left(a_{0}\right) >0$. This may serve as the master equation in all stability problems for the cylindrical thin-shell wormholes.
The existing solutions to the Einstein equations describing rotating cylindrical wormholes are not asymptotically flat and therefore cannot describe wormhole entrances as local objects in our Universe. To overcome this difficulty, flat asymptotic regions are added to wormhole solutions by matching them at some surfaces $Σ_-$ and $Σ_+$. It is shown, however, that if the wormhole solution is obtained for scalar fields with arbitrary potentials, possibly interacting with an azimuthal electric or magnetic field, then the matter content of one or both thin shells appearing on $Σ_-$ and $Σ_+$ violat…
In this article we study a general class of non-rotating thin-shell wormholes with cylindrical symmetry. We consider two physically sound definitions of the flare-out condition and we show that the less restrictive one allows for the construction of wormholes with positive energy density at the throat. We also analyze the mechanical stability of these objects under perturbations preserving the symmetry, proving that previous results are particular cases of a general property. We present examples of wormholes corresponding to Einstein-Maxwell spacetimes.
In this article we investigate cylindrical thin-shell wormholes which are asymptotically anti-de Sitter. We analyze their stability under perturbations preserving the symmetry by using two different methods. We compare the results with those corresponding to the wormholes constructed from the Levi-Civita spacetime. We find that the configurations always require the presence of exotic matter at the throat, and, in the case of the linearized stability analysis, they can be stable for suitable values of the parameters
In continuation of a preceding work on introducing asymmetric thin-shell wormholes as an emerging class of traversable wormholes within the context, this time cylindrically symmetric spacetimes are exploited to construct such wormholes. Having established a generic formulation, first the Linet-Tian metric generally, and then the cosmic string metric and a black string metric in greater details are studied as constructing blocks of cylindrical asymmetric thin-shell wormholes. The corresponding wormholes are investigated within the linearized stability analysis framework to firstly, demonstrate …
Static axisymmetric thin-shell wormholes are constructed within the framework of the Brans-Dicke scalar-tensor theory of gravity. Examples of wormholes associated with vacuum and electromagnetic fields are studied. All constructions must be threaded by exotic matter, except in the case of geometries with a singularity of finite radius, associated with an electric field, which can have a throat supported by ordinary matter. These results are achieved with any of the two definitions of the flare-out condition considered.
In this paper, we apply the cut and paste procedure to charged black string for the construction of thin-shell wormhole. We consider the Darmois-Israel formalism to determine the surface stresses of the shell. We take Chaplygin gas to deal with the matter distribution on shell. The radial perturbation approach (preserving the symmetry) is used to investigate the stability of static solutions. We conclude that stable static solutions exist both for uncharged and charged black string thin-shell wormholes for particular values of the parameters.
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 $Σ_-$ and $Σ_+$. 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 t…
This brief review discusses the existence conditions of wormhole throats and wormholes as global configurations in general relativity under the assumptions of cylindrical and axial symmetries. It is pointed out, in particular, that wormhole throats can exist in static, cylindrically symmetric space-times under slightly different conditions as compared with spherical symmetry. In cylindrical space-time with rotation, throats can exist in the presence of ordinary matter or even in vacuum; however, there are substantial difficulties in obtaining asymptotically flat wormhole configurations without…
A general formalism for the dynamics of non rotating cylindrical thin-shell wormholes is developed. The time evolution of the throat is explicitly obtained for thin-shell wormholes whose metric has the form associated to local cosmic strings. It is found that the throat collapses to zero radius, remains static or expands forever, depending only on the sign of its initial velocity.
In this work, we consider a vacuum solution of Kaluza-Klein theory with cylindrical symmetry. We investigate the physical properties of the solution as viewed in four dimensional spacetime, which turns out to be a stationary, cylindrical wormhole supported by a scalar field and a magnetic field oriented along the wormhole.We then apply a boost to the five dimensional solution along the extra dimension, and perform the Kaluza-Klein reduction. As a result, we show that the new solution is still a wormhole with a radial electric field and a magnetic field stretched along the wormhole throat.
The well-known problem of wormholes in general relativity (GR) is the necessity of exotic matter, violating the Weak Energy Condition (WEC), for their support. This problem looks easier if, instead of island-like configurations, one considers string-like ones, among them, cylindrically symmetric space-times with rotation. However, for cylindrical wormhole solutions a problem is the lacking asymptotic flatness, making it impossible to observe their entrances as local objects in our Universe. It was suggested to solve this problem by joining a wormhole solution to flat asymptotic regions at some…
A new exact vacuum solution in five dimensions, which describes a magnetized cylindrical wormhole in $3+1$ dimensions is presented. The magnetic field lines are stretched along the wormhole throat and are concentrated near to it. We study the motion of neutral and charged test particles under the influence of the magnetized wormhole. The effective potential for a neutral test particle around and across the magnetized wormhole has a repulsive character. The gravitational lensing for the magnetized wormhole for various lens parameters are calculated and compared. The total magnetic flux on eithe…
We determine the electrostatic self-force at rest in an arbitrary static metric with cylindrical symmetry in the linear approximation in the Newtonian constant. In linearised Einstein theory, we express it in terms of the components of the energy-momentum tensor.
We construct traversable thin-shell wormholes in the Dvali-Gabadadze-Porrati theory with cylindrical symmetry applying the cut and paste procedure to a flat black string solution of the five-dimensional vacuum Einstein field equations. In contrast to general relativity case, where thin-shell wormholes violate both weak and null energy conditions, we show that static wormholes are supported by normal matter while vacuum wormholes do not exist.
Given an anisotropic fluid source, we determine in closed forms, upon solving the field equations of general relativity (GR) and teleparallel gravity (TEGR) coupled to a cosmological constant, cylindrically symmetric four-dimensional cosmological rotating wormholes, satisfying all local energy conditions, and cosmological rotating solutions with two axes of symmetry at finite proper distance. These solutions have the property that their angular velocity is proportional to the cosmological constant.
A pointlike electric charge at rest is considered in the spacetime which is a wormhole connecting two otherwise Minkowskian spaces. The potential (i. e. a solution of the Maxwell equations) is split into two parts: one of them depends only on the value and location of the charge, while the other, on the contrary, does not change when the charge is quasistatically moved. Correspondingly, the former is interpreted as being generated by the charge, and the latter as being source-free. It is shown that all source-free potentials differ in the flux through the throat (no "multipoles without multipo…
We consider stationary, cylindrically symmetric configurations in general relativity and formulate necessary conditions for the existence of rotating cylindrical wormholes. It is shown that in a comoving reference frame the rotational part of the gravitational field is separated from its static part and forms an effective stress-energy tensor with exotic properties, which favors the existence of wormhole throats. Exact vacuum and scalar-vacuum solutions (with a massless scalar) are considered as examples, and it turns out that even vacuum solutions can be of wormhole nature. However, solutions…
We describe the analytical extension of certain static cylindrical multi--cosmic string metrics to wormhole spacetimes with only one region at spatial infinity, and investigate in detail the geometry of asymptotically Minkowskian wormhole spacetimes generated by one or two cosmic strings. We find that such wormholes tend to lengthen rather than shorten space travel. Possible signatures of these wormholes are briefly discussed.
In this paper we construct and analyze new classes of wormhole and flux tube-like solutions for the 5D vacuum Einstein equations. These 5D solutions possess generic local anisotropy which gives rise to a gravitational running or scaling of the Kaluza-Klein ``electric'' and ``magnetic'' charges of these solutions. It is also shown that it is possible to self-consistently construct these anisotropic solutions with various rotational 3D hypersurface geometries (i.e. ellipsoidal, cylindrical, bipolar and toroidal). The local anisotropy of these solutions is handled using the technique of anholonom…
We construct cylindrical, traversable wormholes with finite radii by taking into account the cut-and-paste procedure for the case of cosmic string manifolds with a positive cosmological constant. Under reasonable assumptions about the equation of state of the matter located at the shell, we find that the wormhole throat undergoes a monotonous evolution provided it moves at a constant velocity. In order to explore the dynamical nonlinear behaviour of the wormhole throat, we consider that the matter at the shell is supported by anisotropic Chaplygin gas, anti-Chaplygin gas, or a mixed of Chaplyg…
The self-interaction for a static point charge in the space-time of a thin-shell wormhole constructed connecting two identical Schwarzschild geometries is calculated in a series expansion. The electrostatic self-force is evaluated numerically. It is found to be attractive towards the throat except for some values of the throat radius proximate to the value of the Schwarzschild horizon for which the force is repulsive or attractive depending on the position of the charge. The result differs from the self-force in the space-time of the Schwarzschild black hole, where it is always repulsive from …
We seek wormholes among rotating cylindrically symmetric configurations in general relativity. Exact wormhole solutions are presented with such sources of gravity as a massless scalar field, a cosmological constant, and a scalar field with an exponential potential. However, none of these solutions are asymptotically flat, which excludes the existence of wormhole entrances as local objects in our Universe. To overcome this difficulty, we try to build configurations with flat asymptotic regions using the cut-and-paste procedure: on both sides of the throat, a wormhole solution is matched to a pr…
In this paper, we construct thin-shell wormholes from charged black string through cut and paste procedure and investigate its stability. We assume modified generalized Chaplygin gas as a dark energy fluid (exotic matter) present in the thin layer of matter-shell. The stability of these constructed thin-shell wormholes is investigated in the scenario of linear perturbations. We conclude that static stable as well as unstable configurations are possible for cylindrical thin-shell wormholes.
Electrostatic Green functions for grounded equipotential circular and elliptical rings, and grounded hyperspheres in n-dimension electrostatics, are constructed using Sommerfeld's method. These electrostatic systems are treated geometrically as different radial p-norm wormhole metrics that are deformed to be the Manhattan norm, namely "squashed wormholes". Differential geometry techniques are discussed to show how Riemannian geometry plays a rule in Sommerfeld's method. A comparison is made in terms of strength and position of the image charges for Sommerfeld's method with those for the more c…
The electrostatic self-force on a point charge in cylindrical thin-shell space-times is interpreted as the sum of a $bulk$ field and a $shell$ field. The $bulk$ part corresponds to a field sourced by the test charge placed in a space-time without the shell. The $shell$ field accounts for the discontinuity of the extrinsic curvature ${κ^p}_q$. An equivalent electric problem is stated, in which the effect of the shell of matter on the field is reconstructed with the electric potential produced by a non-gravitating charge distribution of total image charge $Q$, to interpret the shell field in bot…
The Zipoy-Voorhees-Weyl (ZVW) spacetime characterized by mass ($M$) and oblateness ($δ$) is proposed in the construction of viable thin-shell wormholes (TSWs). Departure from spherical / cylindrical symmetry yields positive total energy in spite of the fact that local energy density may take negative values. We show that oblateness of the bumpy sources / black holes can be incorporated as a new degree of freedom that may play role in the resolution of the exotic matter problem in TSWs. Small velocity perturbation reveals, however, that the resulting TSW is unstable.
We obtain the self-interaction for a point charge in the space-time of a cylindrical thin-shell wormhole connecting two identical locally flat geometries with a constant deficit angle. Although this wormhole geometry is locally indistinguishable from a cosmic string background, the corresponding self-forces are different even at the qualitative level. In fact in the cosmic string geometry the force is always repulsive while for the wormhole background we find that the force may point outwards or towards the wormhole throat depending on the parameters of the configuration. These results suggest…
In this short review we present some recently obtained traversable wormhole models in the framework of general relativity (GR) in four and six dimensions that somehow widen our common ideas on wormhole existence and properties. These are, first, rotating cylindrical wormholes, asymptotically flat in the radial direction and existing without exotic matter. The topological censorship theorems are not violated due to lack of asymptotic flatness in all spatial directions. Second, these are cosmological wormholes constructed on the basis of the Lemaitre-Tolman-Bondi solution. They connect two copie…
In this article we construct cylindrical thin-shell wormholes in the context of global cosmic strings. We study the stability of static configurations under perturbations preserving the symmetry and we find that the throat tends to collapse or expand, depending only on the direction of the velocity perturbation.
We compute the exterior Green function for a grounded equi-potential circular ring in two-dimensional electrostatics by treating the system geometrically as a "squashed wormhole" with an image charge located in a novel but obvious position, thereby implementing a method first suggested in 1897 by Sommerfeld. We compare and contrast the strength and location of the image charge in the wormhole picture with that of the conventional point of view where an image charge is located inside the circular ring. While the two viewpoints give mathematically equivalent Green functions, we believe they prov…
We find a family of exact solutions to the Einstein-Maxwell equations for rotating cylindrically symmetric distributions of a perfect fluid with the equation of state $p = wρ$ ($|w| < 1$), carrying a circular electric current in the angular direction. This current creates a magnetic field along the $z$ axis. Some of the solutions describe geometries resembling that of Melvin's static magnetic universe and contain a regular symmetry axis, while some others (in the case $w > 0$) describe traversable wormhole geometries which do not contain a symmetry axis. Unlike Melvin's solution, those with ro…
We continue to study the effect of uneven voltage distribution on two close cylindrical conductors with parallel axes started in our papers [1] and [2], now to find the electrostatic torques. We calculate the electrostatic potential and energy to lowest order in the gap to cylinder radius ratio for an arbitrary relative rotation of the cylinders about their symmetry axis. By energy conservation, the axial torque, independent of the uniform voltage difference, is found as a derivative of the energy in the rotation angle. We also derive both the axial and slanting torques by the surface integrat…
We study the effect of any uneven voltage distribution on two close cylindrical conductors with parallel axes that are slightly shifted in the radial and by any length in the axial direction. The investigation is especially motivated by certain precision measurements, such as the Satellite Test of the Equivalence Principle (STEP). By energy conservation, the force can be found as the energy gradient in the vector of the shift, which requires determining potential distribution and energy in the gap. The boundary value problem for the potential is solved, and energy is thus found to the second o…
We investigate negative tension branes as stable thin shell wormholes in Reissner-Nordstrom-(anti) de Sitter spacetimes in $d$ dimensional Einstein gravity. Imposing Z2 symmetry, we construct and classify traversable static thin shell wormholes in spherical, planar (or cylindrical) and hyperbolic symmetries. In spherical geometry, we find the higher dimensional counterpart of Barcelo and Visser's wormholes, which are stable against spherically symmetric perturbations. We also find the classes of thin shell wormholes in planar and hyperbolic symmetries with a negative cosmological constant, whi…
We continue our study of patch effect (PE) for two close cylindrical conductors with parallel axes, slightly shifted against each other in the radial and by any length in the axial direction, started in [1], where the potential and energy in the gap were calculated to the second order in the small transverse shift, and to lowest order in the gap to cylinder radius ratio. Based on these results, here we derive and analyze PE force. It consists of three parts: the usual capacitor force due to the uniform potential difference, the one from the interaction between the voltage patches and the unifo…
Using the cut-and-paste procedure, we construct static and dynamic plane symmetric wormholes by surgically grafting together two spacetimes of plane symmetric vacuum solutions with a negative cosmological constant. These plane symmetric wormholes may be viewed as domain walls connecting different universes, having planar topology, and upon compactification of one or two coordinates, cylindrical topology or toroidal topology, respectively. A stability analysis is carried out for the dynamic case by taking into account specific equations of state, and a linearized stability analysis around stati…
We compute exterior Green functions for equipotential, grounded hyperspheres in N-dimensional electrostatics by squashing Riemannian wormholes, where an image charge is placed in the branch of the wormhole opposite the branch containing the source charge, thereby providing a vivid geometrical approach to a method first suggested in 1897 by Sommerfeld. We compare and contrast the strength and location of the image charge in the wormhole approach with that of the conventional Euclidean solution where an image charge of reduced magnitude is located inside the hypersphere. While the two approaches…
A regular wormhole solution in gravity coupled with a phantom scalar and electromagnetic fields is found. The solution exists for a special choice of the parameter $f$ of the potential term. The mass $m$ of a wormhole filled with a phantom and electrostatic fields is calculated. It is shown that close to some point $f_0$ a small value of the mass $m$ is the remainder of two big masses of the phantom and electrostatic fields. The connection with the renormalization procedure in quantum filed theory is considered. The connection between Wheeler's idea ``mass without mass'' and renormalization pr…
The MICROSCOPE experiment was designed to test the weak equivalence principle in space, by comparing the low-frequency dynamics of cylindrical "free-falling" test masses controlled by electrostatic forces. We use data taken during technical sessions aimed at estimating the electrostatic stiffness of MICROSCOPE's sensors to constrain a short-range Yukawa deviation from Newtonian gravity. We take advantage of the fact that in the limit of small displacements, the gravitational interaction (both Newtonian and Yukawa-like) between nested cylinders is linear, and thus simply characterised by a stif…
