When bosonic matter in the form of a complex scalar field is added to Ellis wormholes, the phenomenon of spontaneous symmetry breaking is observed. Symmetric solutions possess full reflection symmetry with respect to the radial coordinate of the two asymptotically flat spacetime regions connected by the wormhole, whereas asymmetric solutions do not possess this symmetry. Depending on the size of the throat, at bifurcation points pairs of asymmetric solutions arise from or merge with the symmetric solutions. These asymmetric solutions are energetically favoured. When the backreaction of the boson field is taken into account, this phenomenon is retained. Moreover, in a certain region of the solution space both symmetric and asymmetric solutions exhibit a transition from single throat to double throat configurations.
Analytical wormhole solutions in $U_4$ theory are presented. It is discussed whether the extremely short range repulsive forces, related to the spin angular momentum of matter, could be the ``carrier'' of the exoticity that threads the wormhole throat.
Analytical wormhole solutions in Brans-Dicke theory in the presence of matter are presented. It is shown that the wormhole throat must not be necessarily threaded with exotic matter.
In this paper we study the correspondence between the real part of quasinormal modes (QNMs) and the shadow radius in a wormhole spacetime. Firstly we consider the above correspondence in a static and spherically symmetric wormhole spacetime and then explore this correspondence numerically by considering different wormhole models having specific redshift functions. To this end, we generalize this correspondence to the rotation wormhole spacetime and calculate the typical shadow radius of the rotating wormhole when viewed from the equatorial plane. We argue that due to the rotation and depending…
We show that the violation of the null energy condition by matter, required by traversable wormholes, can be removed in spacetimes with torsion. In addition, we show that this violation can also be removed in the conformal frame obtained by a Weyl transformation. This comes about because both conformally transformed wormholes and wormholes in spacetimes with torsion become sustained thanks to a combination of 'normal' matter, that satisfies the null energy condition, and an induced 'geometric' energy-momentum tensor that is able to greatly violate the null energy condition.
An analitical approximation of $<ϕ^2>$ for a scalar field in a static spherically symmetric wormhole spacetime is obtained. The scalar field is assumed to be both massive and massless, with an arbitrary coupling $ξ$ to the scalar curvature, and in a zero temperature vacuum state.
Geodesic motion in traversable Schwarzschild and Kerr thin-shell wormholes constructed by the cut-and-paste method introduced by Visser (1989 Nucl. Phys. B 328 203; 1995 Wormholes: from Einstein to Hawking (Woodbury, MN: American Institute of Physics)) is studied. The orbits are calculated exactly in terms of elliptic functions and visualized with the help of embedding diagrams.
We analize the stability of a class of thin-shell wormholes with spherical symmetry evolving in flat FRW spacetimes. The wormholes considered here are supported at the throat by a perfect fluid with equation of state $\mathcal{P}=wσ$ and have a physical radius equal to $aR$, where $a$ is a time-dependent function describing the dynamics of the throat and $R$ is the background scale factor. The study of wormhole stability is done by means of the stability analysis of dynamic systems.
The existence of charged black holes has suggested that wormholes may also be charged. The purpose of this paper is to construct a general model of a charged wormhole that proves to be a natural extension of the original Morris-Thorne wormhole. This goal is achieved by means of the classical embedding theory that has played a major role in the general theory of relativity.
The Carminati and McLenaghan (CM) curvature invariants are powerful tools for probing spacetimes. Henry et al. formulated a method of plotting the CM curvature invariants to study black holes. The CM curvature invariants are scalar functions of the underlying spacetime. Consequently, they are independent of the chosen coordinates and characterize the spacetime. For Class B1 spacetimes, there are four independent CM curvature invariants: R, r1, r2, and w2. Lorentzian traversable wormholes and warp drives are two theoretical solutions to Einstein's field equations, which allow faster-than-light …
We study the collision of two particles in the Teo wormhole spacetime, in which the wormhole is stationary and axisymmetric. We show that a non-rotating Teo wormhole cannot be a particle accelerator, while a rotating Teo wormhole can be used to accelerate particles and create high energy collisions because of the deep effective potential of the colliding particles. The process is different from that in the vicinity of a near-extremal black hole, since here there is no event horizon. This is the first example of particle collision with high center-of-mass energy in a spacetime with no event hor…
In a collisional Penrose process, two particles coming from the asymptotically flat region collide in the ergosphere of a compact object. The collision produces two new particles, one with positive energy and one with negative energy. When the particle with positive energy escapes to infinity, the process extracts energy from the compact object. In this paper, we study the collisional Penrose process in a rotating wormhole spacetime. We consider the simple case of a head-on collision at the throat of a Teo wormhole. We find that the process of energy extraction from a Teo wormhole can be subst…
We discuss the problem of wormholes from the viewpoint of gluing together two Reissner--Nordström-type universes while putting between them a segment of the Nariai-type world (in both cases there are also present electromagnetic fields as well as the cosmological constant). Such a toy wormhole represents an example of one-way topological communication free from causal paradoxes, though involving a travel to next spacetime sheet since one has to cross at least a pair of horizons through which the spacetimes' junction occurs. We also consider the use of thin shells in these constructions. Such a…
In order to be traversable, the static Lorentzian wormhole must be made out of some exotic matter that violates the weak energy condition. The quantized fields are the natural candidates as their stress-energy tensor, in many cases, possesses desired properties. In this paper we construct and examine the stress-energy tensor of the quantized massive scalar, spinor and vector fields in six static wormhole spacetimes. We find that in all considered cases the quantum fields violate the Morris-Thorne conditions and do not have the form necessary to support the wormhole throat. This is in concord w…
In this work, we calculate the deflection angle of light in a spacetime that interpolates between regular black holes and traversable wormholes, depending on the free parameter of the metric. Afterwards, this angular deflection is substituted into the lens equations which allows to obtain physically measurable results, such as the position of the relativistic images and the magnifications.
A two-parameter family of spherically symmetric, static Lorentzian wormholes is obtained as the general solution of the equation $ρ=ρ_t=0$, where $ρ= T_{ij} u^iu^j$, $ρ_t = (T_{ij} - {1\over2} T g_{ij}) u^iu^j$, and $u^i u_i =- 1$. This equation characterizes a class of spacetimes which are ``self dual'' (in the sense of electrogravity duality). The class includes the Schwarzschild black hole, a family of naked singularities, and a disjoint family of Lorentzian wormholes, all of which have vanishing scalar curvature (R=0). Properties of these spacetimes are discussed. Using isotropic coordinat…
A generalisation of the asymptotic wormhole boundary condition for the case of spacetimes with a cosmological horizon is proposed. In particular, we consider de Sitter spacetime with small cosmological constant. The wave functions selected by this proposal are exponentially damped in WKB approximation when the scale factor is large but still much smaller than the horizon size. In addition, they only include outgoing gravitational modes in the region beyond the horizon. We argue that these wave functions represent quantum wormholes and compute the local effective interactions induced by them in…
This article deals with the study of the dynamics of particles in different wormhole geometries. Using the Jacobi metric approach we study the geodesic motion on the Morris-Thorne wormhole. We found the only stable circular orbit located at the throat. We show that the Gaussian curvature of the Jacobi metric is directly related with the wormhole flare-out condition. We provide a simple test for determining the existence of a throat in a spacetime by using the Gaussian curvature of the associated Jacobi metric only. We discuss about the trajectories in the Kepler problem in a wormhole backgroun…
We consider the total energy loss and spectral density of uniformly moving electrically charged particles in the spacetime of a wormhole with an infinitely short throat. We show that the total energy loss $\mathcal{E} \sim e^2vγa^2/b^3$, where $γ$ is relativistic factor, $a$ is the radius of the wormhole's throat and $b$ is the impact factor. The spectrum of the energy for particles radially moving through the wormhole's throat $\mathcal{E} \sim e^2vγ/a$. The spectral density of the total energy has a maximum at frequency $ω_m \sim vγ/b$ and at $ω_m \sim vγ/a$ for radial motion.
Static traversable wormhole solutions of the Einstein equations require ``exotic'' matter which violates the weak energy condition. The vacuum stress-energy of quantized fields has been proposed as the source for this matter. Using the Dewitt-Schwinger approximation, analytic expressions for the stress-energy of a quantized massive scalar field are calculated in five static spherically symmetric Lorentzian wormhole spacetimes. We find that in all cases, for both minimally and conformally coupled scalar fields, the stress-energy does not have the properties needed to support the wormhole geomet…
We explore the possibility of dynamic wormhole geometries, within the context of nonlinear electrodynamics. The Einstein field equation imposes a contracting wormhole solution and the obedience of the weak energy condition. Furthermore, in the presence of an electric field, the latter presents a singularity at the throat, however, for a pure magnetic field the solution is regular. Thus, taking into account the principle of finiteness, that a satisfactory theory should avoid physical quantities becoming infinite, one may rule out evolving wormhole solutions, in the presence of an electric field…
We study the geometry of a wormhole spacetime filled with anisotropic matter in the context of general relativity. In the course of the study, new static and spherically symmetric solutions, analytic and numerical ones, are found. We specify the existence condition for a wormhole throat. We analyze properties of the solutions after categorizing them based on the spacetime regularity and the signature of energy density. The necessary conditions which allow a wormhole spacetime to be nonsingular are described.
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,…
In this paper I present a new class of traversable wormholes. This is done by surgically grafting two Schwarzschild spacetimes together in such a way that no event horizon is permitted to form. This surgery concentrates a non--zero stress--energy on the boundary layer between the two asymptotically flat regions. I shall investigate this stress--energy in detail using the "junction condition" formalism. A feature of the present analysis is that this class of traversable wormholes is sufficiently simple for a (partial) dynamical stability analysis to be carried out. The stability analysis places…
We speculate about the spacetime description due to the presence of Lorentzian wormholes (handles in spacetime joining two distant regions or other universes) in quantum gravity. The semiclassical rate of production of these Lorentzian wormholes in Reissner-Nordström spacetimes is calculated as a result of the spontaneous decay of vacuum due to a real tunneling configuration. In the magnetic case it only depends on the field theoretical fine structure constant. We predict that the quantum probability corresponding to the nucleation of such geodesically complete spacetimes should be actually ne…
We consider a non-static evolving version of the regular "black-bounce"/traversable wormhole geometry recently introduced in JCAP02(2019)042 [arXiv:1812.07114 [gr-qc]]. We first re-write the static metric using Eddington-Finkelstein coordinates, and then allow the mass parameter $m$ to depend on the null time coordinate (a la Vaidya). The spacetime metric is \[ ds^{2}=-\left(1-\frac{2m(w)}{\sqrt{r^{2}+a^{2}}}\right)dw^{2}-(\pm 2 \,dw \,dr) +\left(r^{2}+a^{2}\right)\left(dθ^{2}+\sin^{2}θ\;dϕ^{2}\right). \] Here $w=\{u,v\}$ denotes the $\{outgoing,ingoing\}$ null time coordinate; representing $\…
In this paper we study classical general relativistic static wormhole configurations with pseudo-spherical symmetry. We show that in addition to the hyperbolic wormhole solutions discussed by Lobo and Mimoso in the Ref. Phys.\ Rev.\ D {\bf 82}, 044034 (2010), there exists another wormhole class, which is truly pseudo-spherical counterpart of spherical Morris-Thorne wormhole (contrary to the Lobo-Mimoso wormhole class), since all constraints originally defined by Morris and Thorne for spherically symmetric wormholes are satisfied. We show that, for both classes of hyperbolic wormholes the energ…
We study the linear polarization from the accretion disk around a class of static traversable wormholes. Applying the simplified model of a magnetized fluid ring orbiting in the equatorial plane, we search for characteristic signatures, which could distinguish wormhole from black hole spacetimes by their polarization properties. For the purpose we analyse the direct polarized images for different inclination angles, the strongly lensed indirect images, and the polarized radiation which reaches the asymptotic observer through the wormhole throat, and compare to the Schwarzschild black hole. For…
The effects of asymptotically anti-de Sitter wormholes in low-energy field theory are calculated in full detail for three different matter contents: a conformal scalar field, an electromagnetic field and gravitons. There exists a close relation between the choice of vacuum for the matter fields and the selection of a basis of the Hilbert space of anti-de Sitter wormholes. In the presence of conformal matter (i.e., conformal scalar or electromagnetic fields), this relation allows us to interpret the elements of these bases as wormhole states containing a given number of particles. This interpre…
We study the thermodynamic equilibrium of matter in a wormhole `station' which connects various distinct asymptotic regions of a spacetime. An example of the `station' is a traversable wormhole connecting two distant regions. The temperatures of matter in the `station' measured at various asymptotic regions are not necessarily the same. We propose a generalized `temperature' which characterizes the thermal equilibrium in the spacetime with the `station'. We additionally discuss how thermal `equilibrium' works for a multiply connected spacetime.
An $n$-dimensional Riemannian space is said to be of embedding class $m$ if $n+m$ is the lowest dimension of the flat space in which the given space can be embedded. A spherically symmetric spacetime of class two can be reduced to class one by a suitable transformation of coordinates. Applied to wormholes, given a well-defined shape function $b=b(r)$, the resulting wormhole has an event horizon and is therefore nontraversable. On a macroscopic scale, $b(r)$ can be replaced by $m(r)$, the effective mass of a spherical star of radius $r$ with $m(0)=0$, to yield a valid solution. Spacetimes of em…
Wormholes in Einstein-Dirac-Maxwell theory with identical spacetime asymptotics
Al-Farabi Kazakh National University（阿尔法拉比哈萨克国立大学）；Academician J. Jeenbaev Institute of Physics of the NAS of the Kyrgyz Republic（吉尔吉斯共和国国家科学院J. Jeenbaev院士物理研究所）
We calculate the vacuum average value of the field square and the stress-energy tensor of a massive scalar field, with non-minimal coupling $ξ$ to the curvature in the short-throat flat-space wormhole background. The obtained results are not suitable for an analytical analysis and for this reason we provide a numerical analysis for different values of the coupling constant, $ξ$. It was shown that the vacuum polarization cannot self-consistently support the wormhole. Otherwise, the energy-momentum tensor does not violate the null energy condition near the throat.
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 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…
Stability regions of glued wormholes with massless Kim-Lee backreacted spacetimes as interior
Zel’dovich International Center for Astrophysics, Bashkir State Pedagogical University（泽尔多维奇天体物理国际中心，巴什基尔国立师范大学）；Department of Mathematics, Kidderpore College（基德波尔学院数学系）
The general parametrization for spacetimes of spherically symmetric Lorentzian, traversable wormholes in an arbitrary metric theory of gravity is presented. The parametrization is similar in spirit to the post-Newtonian parametrized formalism, but with validity that extends beyond the weak field region and covers the whole space. Our method is based on a continued-fraction expansion in terms of a compactified radial coordinate. Calculations of shadows and quasinormal modes for various examples of parametrization of known wormhole metrics that we have performed show that, for most cases, the pa…
The embedding of a curved spacetime in a higher-dimensional flat spacetime has continued to be a topic of interest in the general theory of relativity, as exemplified by the induced-matter theory. This paper deals with spacetimes of embedding class one, i.e., spacetimes that can be embedded in a five-dimensional flat spacetime. Einstein's theory allows the fifth dimension to be either spacelike or timelike. By assuming the latter, this paper addresses two fundamental issues concerning Morris-Thorne wormholes, the origin of exotic matter and the frequently inexplicable enormous radial tension a…
It is well known that solutions of general relativity which allow for traversable wormholes require the existence of exotic matter (matter that violates weak or null energy conditions [WEC or NEC]). In this article, we provide a class of exact solution for Einstein-Maxwell field equations describing wormholes assuming the erstwhile cosmological term $Λ$ to be space variable, viz., $Λ= Λ(r)$. The source considered here not only a matter entirely but a sum of matters i.e. anisotropic matter distribution, electromagnetic field and cosmological constant whose effective parts obey all energy condit…
We consider the self-energy and the self-force for scalar massive and massless particles at rest in the wormhole space-time. We develop a general approach to obtain the self-force and apply it to the two specific profiles of the wormhole throat, namely, with singular and with smooth curvature. We found that the self-force changes its sign at the point where nonminimal coupling $ξ= 1/8$ (for massless case) and it tends to infinity for specific values of $ξ$. It may be attractive as well repulsive depending on the profile of the throat. For massless particle and minimal coupling case the electro…
Spacetime wormholes in isotropic spacetimes are represented traditionally by embedding diagrams which were symmetric paraboloids. This mirror symmetry, however, can be broken by considering different sources on different sides of the throat. This gives rise to an asymmetric thin-shell wormhole, whose stability is studied here in the framework of the linear stability analysis. Having constructed a general formulation, using a variable equation of state and related junction conditions, the results are tested for some examples of diverse geometries such as the cosmic string, Schwarzschild, Reissn…
We investigate the role of a specifically warped extra dimension in constructing examples of higher dimensional spacetimes representing Lorentzian wormholes. The warping chosen is largely inspired by the well-known non-static Witten bubble of nothing, though our spacetimes are static and geometrically different. Vacuum solutions in $D\geq 5$ dimensions and others (non-asymptotically flat) with `perfectly normal' matter stress energy are interpreted as possible Lorentzian wormholes. Asymptotically flat wormholes in $D\geq 5$ with `exotic matter' and within this class of spacetimes also appear t…
In this paper, we investigate the role of gravito-inertial effects on the Casimir energy of a massless scalar field confined between two parallel plates orbiting a static and zero tidal Schwarzschild-like wormhole, at zero temperature. Firstly, we obtain the metric in isotropic coordinates, finding the allowed angular velocities and the circular orbit radii for a material particle as well as for the photon. Following, we compute the changes induced by both gravity and rotation of the plates in the energy density of the quantum vacuum fluctuations associated to the scalar field, in the zero tid…
We expand upon our previous analysis of numerical moving-puncture simulations of the Schwarzschild spacetime. We present a derivation of the family of analytic stationary 1+log foliations of the Schwarzschild solution, and outline a transformation to isotropic-like coordinates. We discuss in detail the numerical evolution of standard Schwarzschild puncture data, and the new time-independent 1+log data. Finally, we demonstrate that the moving-puncture method can locate the appropriate stationary geometry in a robust manner when a numerical code alternates between two forms of 1+log slicing duri…
In this paper, by setting proper boundaries in the Minkowski spacetime, we construct three toy model spacetimes, a toy black hole, a toy white hole, and a toy wormhole. Based on these model spacetimes, we discuss the Hawking radiation and the information loss problem. By counting the number of the field modes inside and outside the horizon, we show the thermal radiation of the toy black hole. We show that the white hole have a thermal absorption. We show that in the whole toy wormhole spacetime, there is no information lost. In addition, we show the black hole radiation and the white hole abso…
It is theoretically revealed that, in classical physics of spacetimes with wormholes, there are analogs of wave function reduction events, quantum entanglement and Einstein-Podolsky-Rosen (EPR) experiment. Within the suggested approach, wormholes are specified by a typical microscopic radius of their mouths, and this causes the size effect in operation of wormhole-based time machines (closed timelike curves; CTCs). For geometric reasons, classical solid balls in a spacetime with a wormhole are divided into the two categories: small and large balls whose traverse through wormholes is permitted …
A wormhole is constructed by cutting and joining two spacetimes satisfying the low energy string equations with a dilaton field. In spacetimes described by the "string metric" the dilaton energy-momentum tensor need not satisfy the weak or dominant energy conditions. In the cases considered here the dilaton field violates these energy conditions and is the source of the exotic matter required to maintain the wormhole. There is also a surface stress-energy, that must be produced by additional matter, where the spacetimes are joined. It is shown that wormholes can be constructed for which this a…
A simple model of spacetime foam, made by $N$ wormholes in a semiclassical approximation, is taken under examination. We show that the qualitative behaviour of the fluctuation of the metric conjectured by Wheeler is here reproduced.
The static traversable wormhole should made out of some type of exotic matter which satisfies the Morris-Thorne conditions. Although the characteristic size of the region with the exotic matter can be made arbitrary small, the calculations performed so far suggest that the Morris-Thorne conditions are quite restrictive and it is hard to find matter with the desired properties. Traditionally, the quantized fields are considered as the best candidates because they can violate the weak-energy condition. In this paper we employ the Schwinger-DeWitt expansion to construct and examine the approximat…
In the present work we investigate evolving wormhole configurations described by a constant redshift function in Einstein-Cartan theory ({\sf ECT}). The matter content consists of a Weyssenhoff fluid along with an anisotropic matter which together generalize the anisotropic energy momentum tensor in general relativity ({\sf GR}) in order to include the effects of intrinsic angular momentum (spin) of particles. Using a generalized Friedmann-Robertson-Walker ({\sf FRW}) spacetime, we derive analytical evolving wormhole geometries by assuming a particular equation of state ({\sf EoS}) for energy …
