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, the signature of the dark energy equation of state in the echo spectrum can serve as a local measurement of the dark energy.
An analytical solution representing traversable asymptotically flat and symmetric wormholes was obtained without adding exotic matter in two different theories independently: in the Einstein-Maxwell-Dirac theory and in the second Randall-Sundrum brane-world model. Further, a smooth normalizable asymmetric wormhole solution has been recently obtained numerically in the Einstein-Maxwell-Dirac theory. Using the time-domain integration method we study quasinormal ringing of all these wormholes with emphasis to the regime of mimicking the near extremal Reissner-Nordström black holes, which is chara…
Structure at the horizon scale of black holes would give rise to echoes of the gravitational wave signal associated with the post-merger ringdown phase in binary coalescences. We study the waveform of echoes in static and stationary, traversable wormholes in which perturbations are governed by a symmetric effective potential. We argue that echoes are dominated by the wormhole quasinormal frequency nearest to the fundamental black hole frequency that controls the primary signal. We put forward an accurate method to construct the echoes waveform(s) from the primary signal and the quasinormal fre…
The time evolution of the field perturbations in the wormhole and black bounce backgrounds are investigated. We find that the asymmetry of spacetime results in the asymmetry of the effective potential of the perturbed equation. The quasinormal modes are strongly dependent on the shapes of the effective potentials. Specifically, the signals of echoes arise in some wormhole cases and reflect the asymmetric properties of wormholes. We examine the features of echoes within different circumstances. Besides, the negative values of effective potentials usually imply the instability of the system. By …
Here we propose a simple explanation why echoes from wormholes mimicking black holes may be so small that they cannot be observed. The essence of the effect is in the redistribution of the initial energy of gravitational wave among multiple universes, connected by a wormhole.
Echoes are known as modifications of the usual quasinormal ringing of a black hole at late times because of the deviation of space-time from the initial black-hole geometry in a small region near its event horizon. We consider a class of brane-world model solutions of the Shiromizu-Maeda-Sasaki equations, which describe both black holes and wormholes and interpolate between them via a continuous parameter. In this way the brane-world scenario provides a natural model for wormholes mimicking the black hole behavior if the continuous parameter is chosen near the threshold with a black-hole solut…
We have studied the stability of wormhole geometries, under massless scalar, electromagnetic and axial gravitational perturbations, in the context of higher dimensional spacetimes. Intriguingly, the construction of a wormhole spacetime in the presence of higher dimensions, known as braneworld wormholes, \emph{does not} require the existence of exotic matter fields, unlike the scenario in four spacetime dimensions. Being a nonvacuum spacetime, the effective potential experienced by the axial gravitational perturbation differs considerably from the scenarios involving black holes. In particular,…
It has been recently shown that observing pulses isolated from the gravitational radiation transient (also known as echoes) would prove the existence of exotic compact objects (ECOs). Many features of the ringdown signal can be reproduced by simulating a scattering problem instead of the full coalescence of ECOs. In this paper, we study the dynamics of scalar and tensor wavepackets colliding against a spherically symmetric Morris-Thorne wormhole. Our aim is to extract the features of the time-dependent scattering solutions inside and outside the effective potential cavity in addition to their …
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.
A possible cause of the late-time cosmic acceleration is an exotic fluid with an equation of state lying within the phantom regime, i.e., $w=p/ρ<-1$. The latter violates the null energy condition, which is a fundamental ingredient in wormhole physics. Thus, cosmic phantom energy may, in principle, provide a natural fluid to support wormholes. In this work, we find new asymptotically flat wormhole solutions supported by the phantom energy equation of state, consequently extending previous solutions. Thus, there is no need to surgically paste the interior wormhole geometry to an exterior vacuum …
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…
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.
We revisit a family of ultra-static Lorentzian wormholes which includes Ellis-Bronnikov spacetime as a special case. We first show how the required total matter stress energy (which violates the local energy conditions) may be split into a part due to a phantom scalar and another extra piece (which vanishes for Ellis--Bronnikov) satisfying the Averaged Null Energy Condition (ANEC) along radial null geodesics. Thereafter,we examine the effective potential for scalar wave propagation in a general setting. Conditions on the metric function, for which the effective potential may have double barrie…
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 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.
We obtain a family of regular static, spherically symmetric solutions in Einstein--Cartan theory with an electromagnetic field and a nonminimally coupled scalar field with the correct sign of kinetic energy density. At different values of its parameters, the solution, being asemptotically flat at large values of the radial coordinate, describes (i) twice asemptotically flat symmetric wormholes, (ii) asymmetric wormholes with an AdS asymptotic at the "far end", (iii) regular black holes with an extremal horizon or two simple horizons, and (iv) black universes with a de Sitter asymptotic at the …
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.
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 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…
Gravitational wave echoes can be used as a significant observable to understand the properties of black holes horizon. In addition, echoes would also closely relate to the unique properties of compact objects. In this work we study the evolution of electromagnetic field and scalar field under the background of novel black-bounce spacetimes. Our results show an obvious echoes signal that can characterize the properties of novel black-bounce spacetimes, and a detailed analysis about the characteristics of the echoes signal is given. By studying the quasinormal ringdown of the three states of nov…
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…
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…
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 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…
Scalar-tensor theory predicts solutions to the gravitational field equations which describe compact objects in the presence of a non-minimally coupled scalar field to the Einstein tensor. These objects are black holes with scalar hair and wormholes supporting scalar phantom matter. The evolution of test fields in fixed asymptotically-flat backgrounds of exotic compact objects leads to the formation of echoes in the ringdown signal, which designate the existence of trapping regions close to the event horizon. Here, we consider minimally-coupled test scalar fields propagating on compact object s…
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…
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.
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.…
We study specific features of the scattering of gravitational waves on wormholes and normal matter objects. We derive and solve the GW energy transport equation and show that the scattered signal lies in the same frequency spectrum bands as the basic signal. The scattering forms specific long living tails which always accompany the basic signal and have a universal form. The scattering on normal matter objects forms tails which have always the retarding character, while wormholes lead to advanced tails as well. In addition, wormholes may produce considerably stronger effect, when the total ene…
We present an unified approach for the study of idealized gravitational compact objects like wormholes and horizonless stars, here simulated by the presence of boundary conditions at a deeply inner wall. At classical level, namely neglecting quantum effects, the presence of the wall leads to characteristic echoes following the usual ringdown phase, such that it can discriminate black holes from other horizonless, and probably exotic, compact objects. With regard to this issue, an analytical though approximated expression for the complex frequencies of the quasinormal echoes is found and discus…
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.
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.
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…
Simpson and Visser recently proposed a phenomenological way to avoid some kinds of space-time singularities by replacing a parameter whose zero value corresponds to a singularity (say, $r$) with the manifestly nonzero expression $r(u) = \sqrt{u^2 + b^2}$, where $u$ is a new coordinate, and $b =$ \const $>0$. This trick, generically leading to a regular minimum of $r$ beyond a black hole horizon (called a "black bounce"), may hopefully mimic some expected results of quantum gravity, and was previously applied to regularize the Schwarzschild, Reissner-Nordström, Kerr and some other metrics. In t…
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…
We construct explicit examples of globally regular static, spherically symmetric solutions in general relativity with scalar and electromagnetic fields which describe traversable wormholes (with flat and AdS asymptotics) and regular black holes, in particular, black universes. A black universe is a nonsingular black hole where, beyond the horizon, instead of a singularity, there is an expanding, asymptotically isotropic universe. The scalar field in these solutions is phantom (i.e., its kinetic energy is negative), minimally coupled to gravity and has a nonzero self-interaction potential. The …
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…
It is proved that no wormholes can be formed in viable scalar-tensor models of dark energy admitting its phantom-like ($w < -1$) behaviour in cosmology, even in the presence of electric or magnetic fields, if the non-minimal coupling function $f(Φ)$ is everywhere positive and the scalar field $Φ$ itself is not a ghost. Some special static, spherically symmetric wormhole solutions may exist if $f(Φ)$ is allowed to reach zero or to become negative, so that the effective gravitational constant becomes negative in some region making the graviton a ghost. If $f$ remains non-negative, such solutions…
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…
