We first briefly present a consistent world-volume Lagrangian description of lightlike p-branes (LL-branes) in two equivalent forms - a Polyakov-type and a dual to it Nambu-Goto-type formulations. The most important characteristic features of LL-brane dynamics are: (i) the brane tension appears as a non-trivial additional dynamical degree of freedom; (ii) consistency of LL-brane dynamics in a spherically or axially symmetric gravitational background of codimension one requires the presence of an event horizon which is automatically occupied by the LL-brane ("horizon straddling"). Next we consider a bulk Einstein-Maxwell system interacting self-consistently with a codimension one LL-brane. We find spherically symmetric traversable wormhole solutions of Misner-Wheeler type produced by the LL-brane sitting at the wormhole throat with wormhole parameters being functions of the dynamical LL-brane tension.
We shortly outline the principal results concerning the reparametrization-invariant world-volume Lagrangian formulation of lightlike brane dynamics and its impact as a source for gravity and (nonlinear) electromagnetism in black hole and wormhole physics.
The original formulation of the "Einstein-Rosen bridge" in the classic paper of Einstein and Rosen (1935) is historically the first example of a static spherically-symmetric wormhole solution. It is not equivalent to the concept of the dynamical and non-traversable Schwarzschild wormhole, also called "Einstein-Rosen bridge" in modern textbooks on general relativity. In previous papers of ours we have provided a mathematically correct treatment of the original "Einstein-Rosen bridge" as a traversable wormhole by showing that it requires the presence of a special kind of "exotic matter" located …
The Einstein-Rosen "bridge" wormhole solution proposed in the classic paper [1] does not satisfy the vacuum Einstein equations at the wormhole throat. We show that the fully consistent formulation of the original Einstein-Rosen "bridge" requires solving Einstein equations of bulk D=4 gravity coupled to a lightlike brane with a well-defined world-volume action. The non-vanishing contribution of Einstein-Rosen "bridge" solution to the right hand side of Einstein equations at the throat matches precisely the surface stress-energy tensor of the lightlike brane which automatically occupies the thro…
We describe a concise general scheme for constructing solutions of Einstein-Maxwell-Kalb-Ramond gravity-matter system in bulk space-time interacting self-consistently with one or more (widely separated) codimension-one electrically charged lightlike branes. The lightlike brane dynamics is explicitly given by manifestly reparametrization invariant world-volume actions. We present several explicit classes of solutions with different physical interpretation as wormhole-like space-times with one, two or more "throats", singularity-free black holes, brane worlds and space-times undergoing a sequenc…
We consider a self-consistent Einstein-Maxwell-Kalb-Ramond system in the bulk D=4 space-time interacting with a variable-tension electrically charged lightlike brane. The latter serves both as a material and charge source for gravity and electromagnetism, as well as it dynamically generates a bulk space varying cosmological constant. We find an asymmetric wormhole solution describing two "universes" with different spherically symmetric black-hole-type geometries connected through a "throat" occupied by the lightlike brane. The electrically neutral "left universe" comprises the exterior region …
The vacuum polarization of the quantized scalar field with non-conformal coupling $ξ$ on the long throat of a wormhole background is calculated. It is shown that the stress-energy tensor of vacuum fluctuations in considered spacetime is determined by the local geometry of spacetime only. The self-consistent solutions of the semiclassical Einstein field equations describing a long throat of a traversable wormhole are obtained.
Lightlike p-branes (LL-branes) with dynamical (variable) tension allow simple and elegant Polyakov-type and dual to it Nambu-Goto-like world-volume action formulations. Here we first briefly describe the dynamics of LL-branes as test objects in various physically interesting gravitational backgrounds of black hole type, including rotating ones. Next we show that LL-branes are the appropriate gravitational sources that provide proper matter energy momentum tensors in the Einstein equations of motion needed to generate traversable wormhole solutions, in particular, self-consistent cylindrical ro…
The ground state energy of the massive scalar field with non-conformal coupling $ξ$ on the short-throat flat-space wormhole background is calculated by using zeta renormalization approach. We discuss the renormalization and relevant heat kernel coefficients in detail. We show that the stable configuration of wormholes can exist for $ξ> 0.123$. In particular case of massive conformal scalar field with $ξ=1/6$, the radius of throat of stable wormhole $a\approx 0.16/m$. The self-consistent wormhole has radius of throat $a\approx 0.0141 l_p $ and mass of scalar boson $m\approx 11.35 m_p$ ($l_p$ an…
A wormhole with a quantum throat on the basis of an approximate model of the spacetime foam is presented. An effective spinor field is introduced for the description of the spacetime foam. The consequences of such model of the wormhole is preventing a "naked'' singularity in the Reissner-Nordström solution with $|e|/m > 1$.
We study in some detail the properties of the mathematically correct formulation of the classical Einstein-Rosen "bridge" as proposed in the original 1935 paper, which was shown in a series of previous papers of ours to represent the simplest example of a static spherically symmetric traversable lightlike thin-shell wormhole. Thus, the original Einstein-Rosen "bridge" is not equivalent to the concept of the dynamical and non-traversable Schwarzschild wormhole, also called "Einstein-Rosen bridge" in modern textbooks on general relativity. The original Einstein-Rosen "bridge" requires the presen…
Traversable wormholes have traditionally been viewed as intrinsically topological entities in some multiply connected spacetime. Here, we show that topology is too limited a tool to accurately characterize a generic traversable wormhole: in general one needs geometric information to detect the presence of a wormhole, or more precisely to locate the wormhole throat. For an arbitrary static spacetime we shall define the wormhole throat in terms of a 2-dimensional constant-time hypersurface of minimal area. (Zero trace for the extrinsic curvature plus a "flare-out" condition.) This enables us to …
We study supergravity instantons sourced by axion (and saxion) fields in the Euclidean $AdS_3\times S^3 \times CY_2$ vacua of IIB supergravity. Such instantons are described by geodesic curves on the moduli space; the timelike geodesics can describe Euclidean wormholes, the lightlike geodesics describe (generalisations of) D-instantons and spacelike geodesics are sub-extremal versions thereof. We perform a concrete classification of such geodesics and find that, despite earlier claims, the wormholes fail to be regular. A subclass of the lightlike geodesics is supersymmetric and, up to dualitie…
Consistent Lagrangian description of lightlike p-branes (LL-branes) is presented in two equivalent forms - a Polyakov-type formulation and a dual to it Nambu-Goto-type formulation. An important characteristic feature of the LL-branes is that the brane tension appears as a non-trivial additional dynamical degree of freedom. Next, properties of p=2 LL-brane dynamics (as a test brane) in D=4 Kerr or Kerr-Newman gravitational backgrounds are discussed in some detail. It is shown that the LL-brane automatically positions itself on the horizon and rotates along with the same angular velocity. Finall…
The aim of the present paper is two-fold. First we describe the Lagrangian dynamics of a recently proposed new class of lightlike p-branes and their interactions with bulk space-time gravity and electromagnetism in a self-consistent manner. Next, we discuss the role of lightlike branes as natural candidates for wormhole "throats" and exemplify the latter by presenting an explicit construction of a new type of asymmetric wormhole solution where the lightlike brane connects a "right" universe with Reissner-Nordstroem geometry to a "left" Bertotti-Robinson universe with two compactified space dim…
We consider Einstein-Maxwell-Kalb-Ramond gravity-matter system in bulk space-time interacting self-consistently with two (widely separated) codimension-one electrically charged lightlike branes. The lightlike brane dynamics is explicitly given by manifestly reparametrization invariant world-volume actions in two equivalent dual to each other formulations (Polyakov-type and Nambu-Goto-type ones) proposed in our previous work. We find an explicit solution of the pertinent Einstein-Maxwell-Kalb-Ramond-lightlike-brane equations of motion describing a "two-throat" wormhole-like space-time consistin…
We demonstrate that rotating matter sets the throat of an Ellis wormhole into rotation, allowing for wormholes which possess full reflection symmetry with respect to the two asymptotically flat spacetime regions. We analyze the properties of this new type of rotating wormholes and show that the wormhole geometry can change from a single throat to a double throat configuration. We further discuss the ergoregions and the lightring structure of these wormholes.
Smooth-throat wormholes are treated on as possessing quantum fluctuation energy with scalar massive field as its source. Heat kernel coefficients of the Laplace operator are calculated in background of the arbitrary-profile throat wormhole with the help of the zeta-function approach. Two specific profile are considered. Some arguments are given that the wormholes may exist. It serves as a solution of semiclassical Einstein equations in the range of specific values of length and certain radius of wormhole's throat and constant of non-minimal connection.
The null geodesic congruence for the Lorentzian version of Hawking's wormhole is studied, in spherical Rindler coordinates. One finds that the wormhole throat expands exponentially and the "flare - out" condition is satisfied. A time reversal is equivalent with an inversion applied to the radial coordinate. The stress energy is mostly located near wormhole's throat and the anisotropic fluid is comoving with the spherical distribution of accelerating observers. Far from the throat (the light cone in Cartesian coordinates) the negative energy density acquires an expression similar with the Casim…
We construct numerically the symmetric non-Abelian wormholes which are supported by a phantom field in the Einstein-Yang-Mills-Higgs theory beyond Bogomol'nyi-Prasad-Sommerfield (BPS) limit where the Higgs self-interaction constant $λ$ is non-vanishing. Analogous to the BPS limit, the probe limit is the Yang-Mills-Higgs field in the background of the Ellis wormhole when the gravity is switched off. In the presence of gravity, the wormhole solutions possess the Yang-Mills-Higgs hair where families of hairy wormholes solutions emerge from the Ellis wormhole when the gravitational coupling consta…
School of Liberal Arts and Sciences, Korea National University of Transportation（韩国国立交通大学人文科学与艺术学院）；Center for Quantum Spacetime, Sogang University（西江大学量子时空中心）
In this paper we study a class of wormhole solutions called generalized Ellis-Bronnikov wormholes in the context of asymptotically safe gravity (ASG). These solutions are characterized by two parameters: an even number $n$ and the wormhole throat radius $r_t$. The particular case $n=2$ recovers the usual Ellis-Bronnikov spacetime, which has already been addressed in the literature. We analyzed the nature of matter in the wormhole's throat, and in nearby regions, of these generalized solutions with $n>2$, using three curvature scalars in the ASG approach, namely, the Ricci scalar, squared Ricci…
We consider Lorentzian wormholes with a phantom field and chiral matter fields. The chiral fields are described by the non-linear sigma model with or without a Skyrme term. When the gravitational coupling of the chiral fields is increased, the wormhole geometry changes. The single throat is replaced by a double throat with a belly inbetween. For a maximal value of the coupling, the radii of both throats reach zero. Then the interior part pinches off, leaving a closed universe and two (asymptotically) flat spaces. A stability analysis shows that all wormholes threaded by chiral fields inherit t…
It was argued in literature that traversable wormholes can exist with arbitrarily small violation of null energy conditions. We show that if the amount of exotic material near the wormhole throat tends to zero, either this leads to a horn instead of a wormhole or the throat approaches the horizon in such a way that infnitely large stresses develop on the throat.
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.
In this work, we consider the full Horndeski Lagrangian applied to wormhole geometries and present the full gravitational field equations. We analyse the general constraints imposed by the flaring-out conditions at the wormhole throat and consider a plethora of specific subclasses of the Horndeski Lagrangian, namely, quintessence/phantom fields, $k$-essence, scalar-tensor theories, covariant galileons, nonminimal kinetic coupling, kinetic gravity braiding, and the scalar-tensor representation of Gauss-Bonnet couplings, amongst others. The generic constraints analysed in this work serve as a co…
A classical membrane model is developed for a dynamic wormhole. Its throat expands hyperbolically with an acceleration proportional to the surface energy density $σ$. The model leads to a negative bulk viscosity coefficient $ζ= - 1/6 π$ on the throat, expressing the instability against perturbations (expansions or contractions).
In this paper, we investigate new exact and analytic solutions of the Einstein Maxwell field equations describing Casimir wormholes with and without the effect of the Generalized Uncertainty Principle (GUP). We consider a specific type of the GUP relations and study three specific models of the redshift function along with two different EoS of state. Here we obtain a class of asymptotically flat Casimir wormhole solutions with and without GUP corrections under the effect of electric charge. Furthermore we check the null, weak, strong and dominant energy conditions at the wormhole throat of rad…
A thin-shell wormhole is crafted by the cut-and-paste method of two Bardeen de-Sitter black holes using Darmois-Israel formalism. Energy conditions are considered for different values of magnetic charge while both mass and cosmological constant are fixed. The attractive and repulsive characteristics of the throat of the thin-shell wormhole are also examined through the radial acceleration. Dynamics and stability of the wormhole are studied around the static solutions of the linearized radial perturbations at the throat of the wormhole. The regions of stability are determined by checking out th…
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…
In this paper, we introduce the $n$-dimensional Lorentzian wormhole solutions of third order Lovelock gravity. In contrast to Einstein gravity and as in the case of Gauss-Bonnet gravity, we find that the wormhole throat radius, $r_0$, has a lower limit that depends on the Lovelock coefficients, the dimensionality of the spacetime and the shape function. We study the conditions of having normal matter near the throat, and find that the matter near the throat can be normal for the region $r_0 \leq r \leq r_{\max}$, where $r_{\max}$ depends on the Lovelock coefficients and the shape function. We …
We consider Ellis wormholes immersed in rotating matter in the form of an ordinary complex boson field. The resulting wormholes may possess full reflection symmetry with respect to the two asymptotically flat spacetime regions. However, there arise also wormhole solutions where the reflection symmetry is broken. The latter always appear in pairs. We analyse the properties of these rotating wormholes and show that their geometry may feature single throats or double throats. We also discuss the ergoregions and the lightring structure of these wormholes.
Recently several models of traversable wormholes have been proposed which require only arbitrarily small amounts of negative energy to hold them open against self-collapse. If the exotic matter is assumed to be provided by quantum fields, then quantum inequalities can be used to place constraints on the negative energy densities required. In this paper, we introduce an alternative method for obtaining constraints on wormhole geometries, using a recently derived quantum inequality bound on the null-contracted stress-energy averaged over a timelike worldline. The bound allows us to perform a sim…
We examine the quantum null energy condition (QNEC) for a $2+1$-dimensional conformal field theory (CFT) at strong coupling in the background of a wormhole spacetime by employing the AdS/CFT correspondence. First, we numerically construct a novel $3+1$-dimensional vacuum AdS black hole solution with non-trivial topology, which is dual to a wormhole geometry connecting two flat universes. Although the bulk null energy condition (NEC) is not violated, the NEC for the holographic stress-energy tensor is violated near the wormhole throat. Next, we investigate the entanglement entropy for a half-sp…
We present a static and axisymmetric traversable wormhole spacetime with vanishing Arnowitt-Deser-Misner (ADM) mass which is characterized by a length parameter $l$ and a deformation parameter $a$ and reduces to the massless Kerr vacuum wormhole as $l\to 0$. The spacetime is analytic everywhere and regularizes a ring-like conical singularity of the massless Kerr wormhole by virtue of a localized exotic matter which violates the standard energy conditions only near the wormhole throat. In the spherically symmetric case ($a=0$), the areal radius of the wormhole throat is exactly $l$ and all the …
The properties of a particular Misner - Thorne wormhole are investigated. The "exotic stress-energy" needed to maintain the wormhole open corresponds to a massless scalar field whose Lagrangean density contains a negative kinetic term. While the Komar energy of the spacetime is vanishing due to the negative energy density and radial pressure, the ADM energy is (minus) the Planck energy. The timelike geodesics are hyperbolae and any static observer is inertial. The null radial trajectories are also hyperbolae and Lorentz invariant as Coleman- de Luccia expanding bubble or Ipser-Sikivie domain w…
Novel wormholes are obtained in Einstein-scalar-Gauss-Bonnet theory for several coupling functions. The wormholes may feature a single-throat or a double-throat geometry and do not demand any exotic matter. The scalar field may asymptotically vanish or be finite, and it may possess radial excitations. The domain of existence is fully mapped out for several forms of the coupling function.
We consider the polymer quantization of the Einstein wormhole throat theory for an eternal Schwarzschild black hole. We numerically solve the difference equation describing the quantum evolution of an initially Gaussian, semi-classical wave packet. As expected from previous work on loop quantum cosmology, the wave packet remains semi-classical until it nears the classical singularity at which point it enters a quantum regime in which the fluctuations become large. The expectation value of the radius reaches a minimum as the wave packet is reflected from the origin and emerges to form a near Ga…
We consider five-dimensional Einstein-Maxwell-Kalb-Ramond system self-consistently coupled to a lightlike 3-brane, where the latter acts as material, charge and variable cosmological constant source. We find wormhole-like solutions whose total space-time manifold consists of either (a) two "universes", which are identical copies of the exterior space-time region (beyond the horizon) of 5-dimensional Schwarzschild-anti-de Sitter black hole, or (b) a "right" "universe" comprising the exterior space-time region of Reissner-Nordstroem-anti-de Sitter black hole and a "left" "universe" being the Rin…
We consider four-dimensional wormholes immersed in bosonic matter. While their existence is based on the presence of a phantom field, many of their interesting physical properties are bestowed upon them by an ordinary complex scalar field, which carries only a mass term, but no self-interactions. For instance, the rotation of the scalar field induces a rotation of the throat as well. Moreover, the bosonic matter need not be symmetrically distributed in both asymptotically flat regions, leading to symmetric and asymmetric rotating wormhole spacetimes. The presence of the rotating matter also al…
We consider the Casimir effect for quantized massive scalar field with non-conformal coupling $ξ$ in a spacetime of wormhole whose throat is rounded by a spherical shell. In the framework of zeta-regularization approach we calculate a zero point energy of scalar field. We found that depending on values of coupling $ξ$, a mass of field $m$, and/or the throat's radius $a$ the Casimir force may be both attractive and repulsive, and even equals to zero.
Probing quantum chaos near a wormhole throat with a circular string
School of Science, Guangxi University of Science and Technology（广西科技大学理学院）；Department of Physics, Institute of Fundamental Physics and Quantum Technology, Ningbo University（宁波大学物理系基础物理与量子技术研究所）；Department of Applied Physics, College of Science, China Agricultural University（中国农业大学理学院应用物理系）
Osaka Institute of Technology（大阪工业大学）；Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）；Kyoto University（京都大学）；Nagoya University（名古屋大学）
Properties of $n(\ge 5)$-dimensional static wormhole solutions are investigated in Einstein-Gauss-Bonnet gravity with or without a cosmological constant $Λ$. We assume that the spacetime has symmetries corresponding to the isometries of an $(n-2)$-dimensional maximally symmetric space with the sectional curvature $k=\pm 1, 0$. It is also assumed that the metric is at least $C^{2}$ and the $(n-2)$-dimensional maximally symmetric subspace is compact. Depending on the existence or absence of the general relativistic limit $α\to 0$, solutions are classified into general relativistic (GR) and non-G…
This paper investigates a particular type of wormhole. The wormhole solutions studied are obtained by sewing together two static, spherically symmetric, charged black-hole metrics at their horizons. The charged wormholes are in a background Kalb-Ramond field, which is the source of the necessary tension in the gravitational field. The metric-tensor elements are studied by numerically solving Einstein's equations with stress-energy-tensor elements given by the combination of static electric and Kalb-Ramond fields. For a certain range of electric charge the tension is positive away from the worm…
