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 rotation and a magnetic field cannot be vacuum and require a current. The wormhole solutions admit matching with flat-space regions on both sides of the throat, thus forming a cylindrical wormhole configuration potentially visible for distant observers residing in flat or weakly curved parts of space. The thin shells, located at junctions between the inner (wormhole) and outer (flat) regions, consist of matter satisfying the Weak Energy Condition under a proper choice of the free parameters of the model, and thus we obtain new examples of phantom-free wormhole models in general relativity. In the limit $w \to 1$, the magnetic field tends to zero, and the wormhole model tends to the one obtained previously, where the source of gravity is stiff matter with the equation of state $p = ρ$.
We construct thin shell wormholes in the magnetic Melvin universe. It is shown that in order to make a TSW in the Melvin spacetime the radius of the throat can not be larger than $\frac{2}{B_{0}}$ in which $B_{0}$ is the magnetic field constant. We also analyze the stability of the constructed wormhole in terms of a linear perturbation around the equilibrium point. In our stability analysis we scan a full set of the Equation of States such as Linear Gas, Chaplygin Gas, Generalized Chaplygin Gas, Modified Generalized Chaplygin Gas and Logarithmic Gas. Finally we extend our study to the wormhole…
We consider a magnetic flux pointing in the $z$ direction of an axially symmetric space-time (Melvin Universe) in a Born-Infeld-type extension of General Relativity (GR) formulated in the Palatini approach. Large magnetic fields could have been produced in the early Universe, and given rise to interesting phenomenology regarding wormholes and black hole remnants. We find a formal analytic solution to this problem that recovers the GR result in the appropriate limits. Our results set the basis for further extensions that could allow the embedding of pairs of black hole remnants in geometries wi…
In the homogeneous and isotropic Friedmann-Robertson-Walker minisuperspace model, it is known that there are no Euclidean wormhole solutions in the pure gravity system. Here it is demonstrated explicitly that in Taub cosmology, which is one of the simplest anisotropic cosmology models, wormhole solutions do exist in pure general relativity in both classical and quantum contexts.
We have proposed a novel shape function on which the metric that models traversable wormholes is dependent. Using this shape function, the energy conditions, equation of state and anisotropy parameter are analyzed in $f(R)$ gravity, $f(R,T)$ gravity and general relativity. Furthermore, the consequences obtained with respect to these theories are compared. In addition, the existence of wormhole geometries is investigated.
In the letter titled ''Traversable Wormholes in General Relativity'' [Phys. Rev. Lett. 128, 091104 (2022)], R. A. Konoplya and A. Zhidenko have constructed an asymmetric wormhole solution, which is not symmetric about the throat and is compounded from smooth gravitational and charged Dirac fields. However, the authors have claimed that a physically relevant condition on the throat is imposed to lead to no gravitational force experienced by a stationary observer at the throat. In this comment, we point out that the above condition is unnecessary.
Wormholes are hypothetical shortcuts in spacetime that in General Relativity unavoidably violate all of the pointwise energy conditions. In this paper, we consider several wormhole spacetimes that, as opposed to the standard \emph{designer} procedure frequently employed in the literature, arise directly from gravitational actions including additional terms resulting from contractions of the Ricci tensor with the metric, and which are formulated assuming independence between metric and connection (Palatini approach). We reinterpret such wormhole solutions under the prism of General Relativity a…
We construct thin-shell electrically charged wormholes in d-dimensional general relativity with a cosmological constant. The wormholes constructed can have different throat geometries, namely, spherical, planar and hyperbolic. Unlike the spherical geometry, the planar and hyperbolic geometries allow for different topologies and in addition can be interpreted as higher-dimensional domain walls or branes connecting two universes. In the construction we use the cut-and-paste procedure by joining together two identical vacuum spacetime solutions. Properties such as the null energy condition and ge…
We consider the construction of generic spherically symmetric thin-shell traversable wormhole spacetimes in standard general relativity. By using the cut-and-paste procedure, we comprehensively analyze the stability of arbitrary spherically symmetric thin-shell wormholes to linearized spherically symmetric perturbations around static solutions. While a number of special cases have previously been dealt with in scattered parts of the literature, herein we take considerable effort to make the analysis as general and unified as practicable. We demonstrate in full generality that stability of the …
Using thin shell formalism we construct two solutions of intra-universe wormholes. The first model is a cosmological analog of the Aichelburg-Schein timehole, while another one is an intra-universe form of the Bronnikov-Ellis solution.
We consider a class of generalized Galileon theories within General Relativity in space-times of more than two spatial dimensions. We show that these theories do not admit stable, static, spherically symmetric, asymptotically flat and traversable Lorentzian wormholes.
Schwarzschild black-hole immersed in an electric or magnetic background in Entangled Relativity
Artemis, Université Côte d’Azur, CNRS, Observatoire Côte d’Azur（阿耳特弥斯，蔚蓝海岸大学，法国国家科学研究中心，蔚蓝海岸天文台）；Bureau des Affaires Spatiales（空间事务局）；Departament de Física Quántica i Astrofísica (FQA), Universitat de Barcelona (UB)（巴塞罗那大学量子物理与天体物理学系）
Recent studies relating the approximations for the equations of state for thin shells and their consequent perturbative evolution are extended to thin-shell wormholes in theories beyond general relativity and more than four spacetime dimensions. The assumption of equations of state of the same form for static and slowly evolving shells appears as a strong restriction excluding the possibility of oscillatory evolutions. Then the new results considerably differ from previous ones obtained within the usual linearized approach.
We consider a way to avoid black hole singularities by gluing a black hole exterior to an interior with a tube-like geometry consisting of a direct product of two-dimensional AdS, dS, or Rindler spacetime with a two-sphere of constant radius. As a result we obtain a spacetime with either "cosmological" or "acceleration" (event) horizons but without an apparent horizon. The inner region is everywhere regular and supported by matter with the vacuum-like equation of state $p_{r}+ρ=0$ where $p_{r}=T_{r}^{r}$ is the longitudinal pressure, $ρ=-T_{0}^{0}$ is the energy density, $T_μ^ν$ is the stress-…
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 [J. Blazquez-Salcedo, C. Knoll, E. Radu, Phys. Rev. Lett. 126 (2021) no.10, 101102] asymptotically flat traversable wormhole solutions were obtained in the Einstein-Dirac-Maxwell theory without using phantom matter. The normalizable numerical solutions found therein require a peculiar behavior at the throat: the mirror symmetry relatively the throat leads to the nonsmoothness of gravitational and matter fields. In particular, one must postulate changing of the sign of the fermionic charge density at the throat, requiring coexistence of particle and antiparticles without annihilation and pos…
An intriguing solution that appears in General Relativity (GR) but has not been observed so far is the wormhole. This exotic solution describes a topological bridge connecting two distinct universes or two different points in the same universe. It is known that the traversable wormhole solutions violate all the energy conditions in GR, resulting in their instability. In this work, we are going to unveil new wormhole solutions for $f(Q)$ gravity where $Q$ is the non-metricity scalar, which is responsible for the gravitational interaction. The energy conditions to constraint these wormhole solut…
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…
We study a static, spherically symmetric wormhole model whose metric coincides with that of the so-called Ellis wormhole but the material source of gravity consists of a perfect fluid with negative density and a source-free radial electric or magnetic field. For a certain class of fluid equations of state, it has been shown that this wormhole model is linearly stable under both spherically symmetric perturbations and axial perturbations of arbitrary multipolarity. A similar behavior is predicted for polar nonspherical perturbations. It thus seems to be the first example of a stable wormhole mo…
In this work, we present the Einstein field equations (EFE) in the framework of a modified matter source and thus find out the solutions for the Wormhole. To obtain characteristic solutions set, we employ two kinds of equations of states (EOS), i.e., the van der Waals and polytropic EOS to the EFE. We adopt embedding class as a general technique for the system and discuss several physical attributes of the stellar system under embedded wormhole solutions. Detailed discussion about the matter contents of the thin-shell developed around the obtained wormhole solutions in the background of Schwar…
It is known that Lorentzian wormholes must be threaded by matter that violates the null energy condition. We phenomenologically characterize such exotic matter by a general class of microscopic scalar field Lagrangians and formulate the necessary conditions that the existence of Lorentzian wormholes imposes on them. Under rather general assumptions, these conditions turn out to be strongly restrictive. The most simple Lagrangian that satisfies all of them describes a minimally coupled massless scalar field with a reversed sign kinetic term. Exact, non-singular, spherically symmetric solutions …
Several traversable wormholes (T-WHs) of the Morris-Thorne type have been presented as exact solutions of Einstein-nonlinear electrodynamics gravity (GR-NLED), e.g. \cite{Arellano2009, Bronnikov2018,Bronnikov_Walia2021, Canate_Breton2018, Canate_Breton_Ortiz2020, Canate_Magos_Breton2020}. However, none of these solutions is support by a nonlinear electrodynamics model satisfying plausible conditions. In this work, we present the first traversable wormhole solution of Einstein-nonlinear electrodynamics gravity coupled to a self-interacting phantom scalar field (GR-NLED-SF) with a NLED model suc…
We derive the simplest traversable wormhole solutions in $n$-dimensional general relativity, assuming static and spherically symmetric spacetime with a ghost scalar field. This is the generalization of the Ellis solution (or the so-called Morris-Thorne's traversable wormhole) into a higher-dimension. We also study their stability using linear perturbation analysis. We obtain the master equation for the perturbed gauge-invariant variable and search their eigenvalues. Our analysis shows that all higher-dimensional wormholes have an unstable mode against the perturbations with which the throat ra…
Wormholes are outstanding solutions of Einstein's General Relativity. They were worked out in the late 1980's by Morris and Thorne, who have figured out a recipe that wormholes must obey in order to be traversable, that is, safely crossed by travelers. A remarkable feature is that General Relativity Theory wormholes must be filled by {\it exotic matter}, which Morris and Thorne define as matter satisfying $-p_r>ρ$, in which $p_r$ is the radial pressure and $ρ$ is the energy density of the wormhole. In the present article, we introduce, for the first time in the literature, traversable wormhole…
Originally proposed as a tool for teaching the general theory of relativity, wormholes are today approached in many different ways and are seeing as an efficient alternative for interstellar and time travel. Attempts to achieve observational signatures of wormholes have been growing as the subject has became more and more popular. In this article we investigate some $f(R,T)$ theoretical predictions for static wormholes, i.e., wormholes whose throat radius can be considered a constant. Since the $T$-dependence in $f(R,T)$ gravity is due to the consideration of quantum effects, a further investi…
The geometry of the Ellis-Bronnikov wormhole is implemented in the Rastall and k-essence theories of gravity with a self-interacting scalar field. The form of the scalar field potential is determined in both cases. A stability analysis with respect to spherically symmetric time-dependent perturbations is carried out, and it shows that in k-essence theory the wormhole is unstable, like the original version of this geometry supported by a massless phantom scalar field in general relativity. In Rastall's theory, it turns out that a perturbative approach reveals the same inconsistency that was fou…
Wormholes are a solution for General Relativity field equations which characterize a passage or a tunnel that connects two different regions of space-time and is filled by some sort of exotic matter, that does not satisfy the energy conditions. On the other hand, it is known that in extended theories of gravity, the extra degrees of freedom once provided may allow the energy conditions to be obeyed and, consequently, the matter content of the wormhole to be non-exotic. In this work, we obtain, as a novelty in the literature, solutions for charged wormholes in the $f(R,T)$ extended theory of gr…
The central theme of this thesis is the study and analysis of black hole mimickers. The concept of a black hole mimicker is introduced, and various mimicker spacetime models are examined within the framework of classical general relativity. The mimickers examined fall into the classes of regular black holes and traversable wormholes under spherical symmetry. The regular black holes examined can be further categorised as static spacetimes, however the traversable wormhole is allowed to have a dynamic (non-static) throat. Astrophysical observables are calculated for a recently proposed regular b…
Morris and Thorne \cite{morris1} proposed traversable wormholes, hypothetical connecting tools, using the concept of Einstein's general theory of relativity. In this paper, the modification of general relativity (in particular $f(R,T)$ theory of gravity defined by Harko et al. \cite{harko}) is considered, to study the traversable wormhole solutions. The function $f(R,T)$ is considered as $f(R,T)=R+αR^2+βT$, where $α$ and $β$ are controlling parameters. The shape and red shift functions appearing in the metric of wormhole structure have significant contribution in the development of wormhole so…
Einstein-Gauss-Bonnet gravity is a generalization of the general relativity to higher dimensions in which the first and second-order terms correspond to general relativity and Einstein-Gauss-Bonnet gravity respectively. We construct a new class of five-dimensional (5D) thin-shell wormholes by the `Cut-Paste' technique from black holes in Einstein-Gauss-Bonnet gravity inspired by non-commutative geometry starting with a static spherically symmetric, Gaussian mass distribution as a source and for this structural form of the thin shell wormhole we have explored several salient features of the sol…
In recent years there has been a growing interest in the field of Casimir wormhole. In classical general relativity (GR), it is known that the null energy condition (NEC) has to be violated to have a wormhole to be stable. The Casimir effect is an experimentally verified effect that is caused due to the vacuum field fluctuations in quantum field theory. Since the Casimir effect provides the negative energy density, thus this act as an ideal candidate for the exotic matter needed for the stability of the wormhole. In this paper, we study the Casimir effect on the wormhole geometry in modified s…
Static, spherically symmetric, traversable wormholes, induced by massless, nonminimally coupled scalar fields in general relativity, are shown to be unstable under spherically symmetric perturbations. The instability is related to blowing-up of the effective gravitational constant on a certain sphere.
We present here analytical solutions of General Relativity that describe evolving wormholes with a non-constant redshift function. We show that the matter that threads these wormholes is not necessarily exotic. Finally, we investigate some issues concerning WEC violation and human traversability in these time-dependent geometries.
We present rotating wormhole solutions in General Relativity, which are supported by a phantom scalar field. These solutions evolve from the static Ellis wormhole, when the throat is set into rotation. As the rotational velocity increases, the throat deforms until at a maximal value of the rotational velocity, an extremal Kerr solution is encountered. The rotating wormholes attain a finite mass and quadrupole moment. They exhibit ergospheres and possess bound orbits.
Static, spherically symmetric, traversable wormhole solutions with electric or magnetic charges are shown to exist in general relativity in the presence of scalar fields nonminimally coupled to gravity. These wormholes, however, turn out to be unstable under spherically symmetric perturbations. The instability is related to blowing-up of the effective gravitational constant on a certain sphere.
The General Theory of Relativity has been an extremely successful theory, with a well established experimental footing, at least for weak gravitational fields. Its predictions range from the existence of black holes, gravitational radiation to the cosmological models, predicting a primordial beginning, namely the big-bang. All these solutions have been obtained by first considering a plausible distribution of matter, and through the Einstein field equation, the spacetime metric of the geometry is determined. However, one may solve the Einstein field equation in the reverse direction, namely, o…
While wormhole spacetimes are predictions of the general theory of relativity, specific solutions may not be compatible with quantum field theory. This paper modifies the charged wormhole model of Kim and Lee with the aim of satisfying an extended version of a quantum inequality due to Ford and Roman. The modified metric may be viewed as a solution of the Einstein field equations representing a charged wormhole that is compatible with quantum field theory.
In this paper, we wish to investigate certain observable effects in the recently obtained wormhole solution of the EiBI theory, which generalizes the zero mass Ellis-Bronnikov wormhole of general relativity. The solutions of EiBI theory contain an extra parameter $κ$ having the inverse dimension of the cosmological constant $Λ$, and is expected to modify various general relativistic observables such as the masses of wormhole mouths, tidal forces and light deflection. A remarkable result is that a non-zero $κ$ could prevent the tidal forces in the geodesic orthonormal frame from becoming arbitr…
We construct examples of static, spherically symmetric wormhole solutions in general relativity with a minimally coupled scalar field $ϕ$ whose kinetic energy is negative in a restricted region of space near the throat (of arbitrary size) and positive far from it. Thus in such configurations a "ghost" is trapped in the strong-field region, which may in principle explain why no ghosts are observed under usual conditions. Some properties of general wormhole models with the $ϕ$ field are revealed: it is shown that (i) trapped-ghost wormholes are only possible with nonzero potentials $V(ϕ)$; (ii) …
