Using a new ansatz for solving the Einstein equations with a scalar field with the sign of the kinetic term inverted, I find a series of formulae to derive axial symmetric stationary exact solutions of the Phantom scalar field in general relativity. We focus on the solutions which represent wormholes. The procedure presented in this work allows to derive new exact solutions up to very simple integrations. Among other results, I find exact rotating solutions containing magnetic monopoles, dipoles, etc., coupled to Phantom scalar and to gravitational multipole fields.
We study the classical Euclidean wormhole solutions for the gravitational systems with minimally coupled pure Phantom field and minimally coupled Phantom field accompanied by perfect fluid. It is shown that such solutions do exist and then the general forms of the Phantom field potential are obtained for which there are classical Euclidean wormhole solutions.
A new solution has been presented for the spherically symmetric space time describing wormholes with Phantom Energy. The model suggests that the existence of wormhole is supported by arbitrarily small quantity of Phantom Energy.
In this paper we derive new static phantom traversable wormholes by assuming a shape function with a quadratic dependence on the radial coordinate r. We mainly focus our study on wormholes sustained by exotic matter with positive energy density (as seen by any static observer) and a variable equation of state $p_r/ρ<-1$, dubbed phantom matter. Among phantom wormhole spacetimes extending to infinity, we show that a quadratic shape function allows us to construct static spacetimes of finite size, composed by a phantom wormhole connected to an anisotropic spherically symmetric distribution of dar…
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.
We extend the notion of phantom energy--which is generally accepted for homogeneously distributed matter with $w<-1$ in the universe--on inhomogeneous spherically symmetric spacetime configurations. A spherically symmetric distribution of phantom energy is shown to be able to support the existence of static wormholes. We find an exact solution describing a static spherically symmetric wormhole with phantom energy and show that a spatial distribution of the phantom energy is mainly restricted by the vicinity of the wormhole's throat. The maximal size of the spherical region, surrounding the thr…
In this article, we have found a series solution of 3D Einstein equations describing a wormhole for an inhomogeneous distribution of phantom energy. Here, we assume equation of state is linear but highly anistropic.
This paper discusses a new variable equation of state parameter leading to exact solutions of the Einstein field equations describing traversable wormholes. In addition to generalizing the notion of phantom energy, the equation of state generates a mathematical model that combines the generalized phantom energy and the generalized Chaplygin gas models.
The purpose of this paper is to obtain exact solutions of the Einstein field equations describing traversable wormholes supported by phantom energy. Their relationship to exact solutions in the literature is also discussed, as well as the conditions required to determine such solutions.
The possible process of creation/annihilation of traversable wormholes in the model with phantom (ghost) scalar field is described. It is shown that such process can be realized only for some special choice of a potential energy, in particular, for the Sine-Gordon potential.
In this paper we study the possibility of sustaining an evolving wormhole via exotic matter made of phantom energy in the presence of a cosmological constant. We derive analytical evolving wormhole geometries by supposing that the radial tension of the phantom matter, which is negative to the radial pressure, and the pressure measured in the tangential directions have barotropic equations of state with constant state parameters. In this case the presence of a cosmological constant ensures accelerated expansion of the wormhole configurations. More specifically, for positive cosmological constan…
We consider the effects of Gravity's Rainbow on the self-sustained equation which is responsible to find new traversable wormholes configurations powered by their own gravitational quantum fluctuations. The form of the shape function considered is obtained by imposing the equation of state $p_{r}=ωρ$. We investigate the size of the wormhole as a function of the parameter $ω$ in the phantom region. We discover that a wormhole which is traversable in principle, but not in practice, can be produced.
A possible candidate for the present accelerated expansion of the Universe is ''phantom energy'', which possesses an equation of state of the form $ω\equiv p/ρ<-1$, consequently violating the null energy condition. As this is the fundamental ingredient to sustain traversable wormholes, this cosmic fluid presents us with a natural scenario for the existence of these exotic geometries. In this context, we shall construct phantom wormhole geometries by matching an interior wormhole solution, governed by the phantom energy equation of state, to an exterior vacuum at a junction interface. Several p…
It is generally agreed that the acceleration of the Universe can best be explained by the presence of dark or phantom energy. The equation of state of the latter shows that the null energy condition is violated. Such a violation is the primary ingredient for sustaining traversable wormholes. This paper discusses wormholes supported by a more general form called polytropic phantom energy. The equation of state results in significant generalizations of the phantom-energy and, in some cases, the generalized Chaplygin-gas wormhole models, both of which continue to receive considerable attention fr…
We study the quasinormal modes for scalar, axial and radial perturbations of massive static spherically symmetric wormholes supported by a phantom scalar field, calculating the modes directly and employing the WKB approximation. The spectrum of the quasinormal modes is compared with the spectrum of Schwarzschild black holes. For fixed multipole number $l$ and large mass $M$ the wormhole modes approach their black hole counterparts as $1/M$.
We have examined the possible construction of a stationary, spherically symmetric and spatially inhomogeneous wormhole spacetime supported by the phantom energy. The later is supposed to be represented by the modified Chaplygin gas equation of state. The solutions so obtained satisfy the flare out and the asymptotic flatness conditions. It is also shown that the averaged null energy condition has to be violated for the existence of the wormhole.
In the present paper we prove a uniqueness theorem for the regular static, traversable wormhole solutions to the Einstein-phantom scalar field theory with two asymptotically flat regions (ends). We show that when a certain condition on the asymptotic values of the scalar field is imposed such solutions are uniquely specified by their mass $M$ and the scalar charge $D$.The main arguments in the proof are based on the positive energy theorem.
Recently, it has been shown by Lobo, Parsaei and Riazi (LPR) that phantom energy with $ω=p_{r}/ρ<-1$ could support phantom wormholes. Several classes of such solutions have been derived by them. While the inner spacetime is represented by asymptotically flat phantom wormhole that have repulsive gravity, it is most likely to be unstable to perturbations. Hence, we consider a situation, where a phantom wormhole is somehow trapped inside a Schwarzschild sphere across a thin shell. Applying the method developed by Garcia, Lobo and Visser (GLV), we shall exemplify that the shell can possess zones o…
In this work we study a Kerr-like wormhole with phantom matter as source. It has three parameters: mass, angular momentum and scalar field charge. This wormhole has a naked ring singularity, other wise it is regular everywhere. The mean feature of this wormhole is that the mouth of the throat lie on a sphere of the same radius as the ring singularity an avoids any observer to see or to reach the singularity, it behaves like an anti-horizon. We analyse the geodesics of the wormhole and find that an observer can go through the geodesics without troubles, but the equator presents an infinity pote…
It has been argued that wormholes are as good a prediction of Einstein's theory as black holes but the theoretical construction requires a reverse strategy, specifying the desired geometric properties of the wormhole and leaving open the determination of the stress-energy tensor. We begin by confirming an earlier result by the author showing that a complete wormhole solution can be obtained by adopting the equation of state $p=ωρ$ and assuming that the wormhole admits a one-parameter group of conformal motions. The main purpose of this paper is to use the assumption of conformal symmetry to sh…
This paper discusses the stability to linearized radial perturbations of spherically symmetric thin-shell wormholes with a "phantom-like" equation of state for the exotic matter at the throat: $P=ωσ$, $ω<0$, where $σ$ is the energy-density of the shell and $P$ the surface pressure. This equation is analogous to the generalized Chaplygin-gas equation of state used by E.F. Eiroa. The analysis, which differes from Eiroa's in its basic approach, is carried out for wormholes constructed from the following spacetimes: Schwarzschild, de Sitter and anti de Sitter, Reissner-Nordstrom, and regular charg…
In this paper we show that, analogously to as it occurs for black holes, there exist three well-defined laws for Lorentzian wormhole thermodynamics and that these laws are related with a thermal phantom-like radiation process coming from the wormhole throat. It is argued that the existence of wormholes could be manifested by means such a radiation. These results are obtained by analyzing the Hayward formalism of spherically symmetric solutions containing trapping horizons, the phenomenon of phantom accretion onto wormholes and the development of phantom thermodynamics.
In this paper we study the possibility of sustaining an evolving wormhole via exotic matter made out of phantom energy. We show that this exotic source can support the existence of evolving wormhole spacetimes. Explicitly, a family of evolving Lorentzian wormholes conformally related to another family of zero-tidal force static wormhole geometries is found in Einstein gravity. Contrary to the standard wormhole approach, where first a convenient geometry is fixed and then the matter distribution is derived, we follow the conventional approach for finding solutions in theoretical cosmology. We d…
Wormholes are tunnels connecting different regions in space-time. They were obtained originally as a solution for Einstein's General Relativity theory and according to this theory they need to be filled by an exotic kind of anisotropic matter. In the present sense, by "exotic matter" we mean matter that does not satisfy the energy conditions. In this article we propose the modelling of wormholes within an alternative gravity theory that proposes an extra material (rather than geometrical) term in its gravitational action. Our solutions are obtained from well-known particular cases of the wormh…
It is concluded in the literature that Ellis wormhole is unstable under small perturbations and would decay either to the Schwarzschild black hole or expand away to infinity. While this deterministic conclusion of instability is correct, we show that the Ellis wormhole reduces to Schwarzschild black hole \textit{only} when the Ellis solution parameter $γ$ assumes a complex value $-i$. We shall then reexamine stability of Ellis and phantom wormholes from the viewpoint of local and asymptotic observers by using a completely different approach, viz., we adapt Tangherlini's nondeterministic, prequ…
Based on the rigid positive energy theorem we proved the uniqueness of static spherically symmetric traversable wormholes with two asymptotically flat ends, being the higher-dimensional solutions of Einstein scalar phantom field. The proof is valid under the auxiliary condition imposed on wormhole mass and scalar charge.
We consider rotating wormhole solutions supported by a complex phantom scalar field with a quartic self-interaction, where the phantom field induces the rotation of the spacetime. The solutions are regular and asymptotically flat. A subset of solutions describing static but not spherically symmetric wormholes is also obtained.
Wormholes (WHs) are considered as hypothetical shortcuts or tunnels in spacetime. In general relativity (GR), the fundamental ingredient of WH geometry is the presence of exotic matter at the throat, which is responsible for the violation of null energy condition (NEC). However, the modified gravity theories has shown to be able to provide WH solutions satisfying energy conditions (ECs). In this paper, we study the static spherically symmetric WH solutions in modified $f(R,T)$ gravity for a phantom fluid case. The exact solutions of this model are obtained through the equation of state (EoS), …
By a combination of analytical and numerical techniques, we demonstrate the existence of spherical, asymptotically flat traversable wormholes supported by exotic matter whose stress tensor relative to the orthonormal frame of Killing observers takes the form of a perfect fluid possessing anisotropic pressures and subject to linear equations of state: $τ=λρc^{2}$, $P=μρc^{2}$. We show that there exists a four parameter family of asymptotically flat spherical wormholes parametrized by the area of the throat A(0), the gradient $Λ(0)$ of the red shift factor evaluated at the throat as well as the …
We prove a uniqueness theorem for traversable wormhole solutions in the Einstein-Maxwell-dilaton gravity with a phantom scalar field and a possible phantom electromagnetic field. In a certain region of the parameter space, determined by the asymptotic values of the scalar field and the lapse function, the regular wormholes are completely specified by their mass, scalar charge and electric charge. The argument is based on the positive energy theorem applied on an appropriate conformally transformed Riemannian space.
In this paper, we study the deflection of light by a class of phantom black hole and wormhole solutions in the weak limit approximation. More specifically, in the first part of this work, we study the deflection of light by Garfinkle-Horowitz-Ströminger black hole and Einstein-Maxwell anti-dilaton black hole using the optical geometry and the Gauss-Bonnet theorem. Our calculations show that gravitational lensing is affected by the phantom scalar field (phantom dilaton). In the second part of this work, we explore the deflection of light by a class of asymptotically flat phantom wormholes. In p…
In Einstein gravity, for an inhomogeneous phantom energy distribution having linear equation of state (but anisotropic), there exists simple exact solution for spherically symmetric space time describing a wormhole. At infinity, the space time is not asymptotically flat and possesses a regular cosmological Killing horizon with an infinite area. In this work, we have shown that, this wormhole solution is also possible in brane world for various matter distribution, which are not necessarily phantom in nature.
The uniqueness of static spherically symmetric traversable wormholes with two asymptotically flat ends, subject to the higher-dimensional solutions of Einstein-Maxwell-phantom dilaton field equations was proved. We considered the case of an arbitrary dilaton coupling constant. Conformal positive energy theorem plays the key role in the considerations.
In this article, we have discussed Morris and Thorne (MT) wormhole solutions in a modified theory of gravity that admits conformal motion. Here we explore the wormhole solutions in $f(R,\,T)$ gravity, which is a function of the Ricci scalar ($R$) and the trace of the stress-energy tensor ($T$). To study wormhole geometries, we make assumption of spherical symmetric static spacetime and the existence of conformal Killing symmetry to get more acceptable astrophysical outcomes. To do this, we choose the expression of $f(R,\,T)$ as $f(R,T)= R+2 γT$. Here we employ the phantom energy EoS relating t…
It has recently been shown that traversable wormholes may be supported by phantom energy. In this work phantom wormhole geometries are modelled by matching an interior traversable wormhole solution, governed by the equation of state $p=ωρ$ with $ω<-1$, to an exterior vacuum spacetime at a finite junction interface. The stability analysis of these phantom wormholes to linearized spherically symmetric perturbations about static equilibrium solutions is carried out. A master equation dictating the stability regions is deduced, and by separating the cases of a positive and a negative surface energ…
We derive and analyze phantom scalar field counterpart to Curzon-Chazy spacetime. Such solution contains 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 spacetime to understand their value in the presence of phantom matter. The electromagnetic generalization of this spacetime is as well briefly considered.
There are a number of reasons to study wormholes with generic cosmological constant $Λ$. Recent observations indicate that present accelerating expansion of the universe demands $Λ>0$. On the other hand, some extended theories of gravitation such as supergravity and superstring theories posses vacuum states with $Λ<0$. Even within the framework of general relativity, a negative cosmological constant permits black holes with horizons topologically different from the usual spherical ones. These solutions are convertible to wormhole solutions by adding some exotic matter. In this paper, the asymp…
We derive an exact wormhole spacetime supported by a phantom scalar field in the context of $f({\sf R})$ gravity. Without specifying the form of the $f({\sf R})$ function, the scalar field self-interacts with a mass term potential that is derived from the scalar equation and the resulting $f({\sf R})$ model is purely supported by the scalar field and it is free of ghosts and avoids the tachyonic instability.
We test the stability of various wormholes and black holes supported by a scalar field with a negative kinetic term. The general axial perturbations and the monopole type of polar perturbations are considered in the linear approximation. Two classes of objects are considered: (i) wormholes with flat asymptotic behavior at one end and AdS on the other (M-AdS wormholes) and (ii) regular black holes with asymptotically de Sitter expansion far beyond the horizon (the so-called black universes). A difficulty in such stability studies is that the effective potential for perturbations forms an infini…
We analyze the properties of a Kerr-like wormhole supported by phantom matter, which is an exact solution of the Einstein-phantom field equations. It is shown that the solution has a naked ring singularity which is unreachable to null geodesics falling freely from the outside. Similarly to Roger Penrose's cosmic censorship, that states that all naked singularities in the Universe must be protected by event horizons, here we conjecture from our results that a naked singularity can also be fully protected by the intrinsic properties of a wormhole's throat.
We provide a new model of higher dimensional wormholes supported by phantom energy derived from a scalar field with negative kinetic term. We have shown that the Averaged Null Energy Condition (ANEC) violating phantom energy can be reduced as desired. We have also noticed that dimension of the spacetime plays a crucial role for measuring the ANEC violating matter needed.
Recently it has been argued that the phantom thin-shell wormholes matched with the Schwarzschild space-time near the Schwarzschild radius ring like Schwarzschild black holes at early times, but differently at late times (arXiv:1602.07309). Here we consider perturbations of the wormhole which was constructed without thin-shells: the Bronnikov-Ellis wormhole supported by the phantom matter and electromagnetic field. This wormhole solution is known to be stable under specific equation of state of the phantom matter. We show that if one does not use the above thin-shell matching, the wormhole, dep…
In this paper, we present an exact solution for $(3+1)$-dimensional Einstein-scalar-Gauss-Bonnet theory (EsGB) in electrovacuum. The solution is characterized by only one parameter, $Q$, which in general can be associated with the electromagnetic field and the scalar field. We show that the solution corresponds to a charged wormhole with throat at the region $r = |Q|$, and is also supported by a real scalar field having a positive kinetic term. We show that the solution belongs to the most general class of solutions known as Ellis wormholes but without the need for `exotic matter' or a phantom…
In the Bogomol'nyi-Prasad-Sommerfield (BPS) limit of Einstein-Yang-Mills-Higgs theory, we construct numerically a non-Abelian wormhole supported by a phantom field. The probe limit is the Yang-Mills-Higgs field in the background of Ellis wormhole when the gravity is switched off. The wormhole solutions possess the Yang-Mills-Higgs hair in the presence of gravity; Thus a branch of hairy wormhole solutions emerge from the Ellis wormhole when the gravitational coupling constant increases. We find that the mass of wormholes and scalar charge of phantom field increase monotonically when the gravita…
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…
We construct explicit examples of globally regular static, spherically symmetric solutions of general relativity with a phantom scalar field as the source of gravity, describing traversable wormholes with flat asymptotic regions on both sides of the throat as well as regular black holes, in particular, those called black universes. To explain why such phantom fields are not observed under usual conditions, we invoke the concept of "invisible ghosts," which means that the phantom field decays quickly enough at infinity and is there too weak to be observed. This approach leads to wormhole models…
It has been suggested that a possible candidate for the present accelerated expansion of the Universe is ''phantom energy''. The latter possesses an equation of state of the form $ω\equiv p/ρ<-1$, consequently violating the null energy condition. As this is the fundamental ingredient to sustain traversable wormholes, this cosmic fluid presents us with a natural scenario for the existence of these exotic geometries. Due to the fact of the accelerating Universe, macroscopic wormholes could naturally be grown from the submicroscopic constructions that originally pervaded the quantum foam. One cou…
We study the time evolution of the test scalar and electromagnetic fields perturbations in configurations of phantom wormholes surrounded by dark energy with state parameter $ω< -1$. We observe obvious signals of echoes reflecting wormholes properties and disclose the physical reasons behind such phenomena. In particular, we find that the dark energy equation of state has a clear imprint in echoes in wave perturbations. When $ω$ approaches the phantom divide $ω=-1$ from below, the delay time of echoes becomes longer. The echo of gravitational wave is likely to be detected in the near future, t…
We investigate a family of inhomogeneous and anisotropic gravitational fields exhibiting a future singularity at a finite value of the proper time. The studied spherically symmetric spacetimes are asymptotically Friedmann-Robertson-Walker at spatial infinity and describe wormhole configurations filled with two matter components: one inhomogeneous and anisotropic fluid and another isotropic and homogeneously distributed fluid, characterized by the supernegative equation of state ω=p/ρ< -1. In previously constructed wormholes, the notion of the phantom energy was used in a more extended sense th…
A possible candidate for the late time accelerated expanding Universe is phantom energy, which possesses rather bizarre properties, such as the prediction of a Big Rip singularity and the violation of the null energy condition. The latter is a fundamental ingredient of traversable wormholes, and it has been shown that phantom energy may indeed sustain these exotic geometries. Inspired by the evolving dark energy parameter crossing the phantom divide, we consider in this work a varying equation of state parameter dependent on the radial coordinate, i.e., $ω(r)=p(r)/ρ(r)$. We shall impose that p…
In 1921 Bach and Weyl derived the method of superposition to construct new axially symmetric vacuum solutions of General Relativity. In this paper we extend the Bach-Weyl approach to non-vacuum configurations with massless scalar fields. Considering a phantom scalar field with the negative kinetic energy, we construct a multi-wormhole solution describing an axially symmetric superposition of $N$ wormholes. The solution found is static, everywhere regular and has no event horizons. These features drastically tell the multi-wormhole configuration from other axially symmetric vacuum solutions whi…
In this work, we have studied accretion of the dark energies onto Morris-Thorne wormhole. For quintessence like dark energy, the mass of the wormhole decreases and phantom like dark energy, the mass of wormhole increases. We have assumed two types of dark energy like variable modified Chaplygin gas (VMCG) and generalized cosmic Chaplygin gas (GCCG). We have found the expression of wormhole mass in both cases. We have found the mass of the wormhole at late universe and this is finite. For our choices the parameters and the function $B(a)$, these models generate only quintessence dark energy (no…
In recent years, cosmic observational data have reported that our present universe is undergoing an accelerated expansion, which has been termed as mysterious "dark energy" phenomena, that is, the origin of dark energy has not been determined yet. According to our previous work that a new equation of state \cite{X.Shan and H.Chen1993} can be employed to explain the dark energy, and we are very interested in investigating the astrophysical scale properties of dark energy based on the new cosmological fluids given that the universe is filled with a dark energy fluid everywhere. Hence, in this pa…
We have found a simple exact solution of spherically-symmetrical Einstein equations describing a wormhole for an inhomogeneous distribution of the phantom energy. The equation of state is linear but highly anisotropic: while the radial pressure is negative, the transversal one is positive. At infinity the spacetime is not asymptotically flat and possesses on each side of the bridge a regular cosmological Killing horizon with an infinite area, impenetrable for any particles. This horizon does not arise if the wormhole region is glued to the Schwarzschild region. In doing so, the wormhole can en…
In this paper we give an electrically charged traversable wormhole solution for the Einstein-Maxwell-dilaton theory when the dilaton is a phantom field, i.e. it has flipped sign kinetic term appearing in the action. In the limit when the charge is zero, we recover the anti-Fisher solution, which can be reduced to the Bronnikov-Ellis solution under certain choices of integration constants. The equations of motion of this theory share the same S-duality invariance of string theory, so the electrically charged solution is rotated into the magnetically charged one by applying such transformations.…
