We reconsider some fundamental problems of the thin shell model. First, we point out that the "cut and paste" construction does not guarantee a well-defined manifold because there is no overlap of coordinates across the shell. When one requires that the spacetime metric across the thin shell is continuous, it also provides a way to specify the tangent space and the manifold. Other authors have shown that this specification leads to the conservation laws when shells collide. On the other hand, the well-known areal radius $r$ seems to be a perfect coordinate covering all regions of a spherically symmetric spacetime. However, we show by simple but rigorous arguments that $r$ fails to be a coordinate covering a neighborhood of the thin shell if the metric across the shell is continuous. When two spherical shells collide and merge into one, we show that it is possible that $r$ remains to be a good coordinate and the conservation laws hold. To make this happen, different spacetime regions divided by the shells must be glued in a specific way such that some constraints are satisfied. We compare our new construction with the old one by solving constraints numerically.
There are several possible choices of the time parameter for the canonical description of a self-gravitating thin shell, but quantum thories built on different time parameters lead to unitarily inequivalent descriptions. We compare the quantum collapse of a thin dust shell in two different times {\it viz.,} the time coordinate in the interior of the shell (originally addressed in \cite{hajicek92a}) and the time coordinate of the comoving observer (proper time). In each case, we obtain exact solutions to the Wheeler-DeWitt equation requiring only a finite and well behaved $U(1)$ current. The tw…
We consider the gravastar model where the vacuum phase transition between the de Sitter interior and the Schwarzschild or Schwarzschild-de Sitter exterior geometries takes place at a single spherical delta-shell. We derive sharp analytic bounds on the surface compactness (2m/r) that follow from the requirement that the dominant energy condition (DEC) holds at the shell. In the case of Schwarzschild exterior, the highest surface compactness is achieved with the stiff shell in the limit of vanishing (dark) energy density in the interior. In the case of Schwarzschild-de Sitter exterior, in additi…
We initiate the hunt for a definition of Hamiltonian constraint in Euclidean Loop Quantum Gravity (LQG) which faithfully represents quantum Dirac algebra. Borrowing key ideas from previous works on Hamiltonian constraint in LQG and several toy models, we present some evidence that there exists such a continuum Hamiltonian constraint operator which is well defined on a suitable generalization of the Lewandowski-Marolf Habitat and is anomaly free off-shell.
In three-dimensional AdS space, we consider the gravitational collapse of dust shell and then investigate the quantum radiation from the collapsing shell by employing the functional Schrödinger formalism. In the formation of the BTZ black hole, the interior geometry of the shell can be chosen as either the massless black hole or the global AdS space. In the incipient black hole limit, we obtain the wave function exactly from the time-dependent Schrödinger equation for a massless scalar field. Then, we show that the occupation number of excited states can be written by analytic expressions, and…
Within 2+1-dimensional cosmological new massive gravity, we consider thin-shell and thin-shell wormhole construction. For this, we introduce first, the junction conditions apt for the fourth order terms in the action of the theory. Then, by employing some specific static solutions in new massive gravity, we study the characteristics of associated thin-shells and thin-shell wormholes. Our finding suggests that, firstly, there cannot exist any thin-shells regarding our chosen solutions of cosmological new massive gravity, and secondly, the constructed thin-shell wormhole does not need to be symm…
We consider a static spherically symmetric thin shell wormhole collides with another thin shell consisting of ordinary matter. By employing the geometrical constraint, which leads to the conservation of energy and momentum, we show that the state after the collision can be solved from the initial data. In the low speed approximation, the solutions are rather simple. The shell may either bounce back or pass through the wormhole. In either case, the wormhole shrinks right after the collision. In the "bouncing" case, a surprising result is that the radial speeds before and after the collision sat…
The study of traversable wormholes is very hot topic for the past 30 years. One of the best possible way to make traversable wormhole is using the thin-shells to cut and paste two spacetime which has tunnel from one region of space-time to another, through which a traveler might freely pass in wormhole throat. These geometries need an exotic matter which involves a stress-energy tensor that violates the null energy condition. However, this method can be used to minimize the amount of the exotic matter. The goal of this thesis study is to study on thin-shell and thin-shell wormholes in general …
In this paper, we construct thin-shell wormholes from charged black string through cut and paste procedure and investigate its stability. We assume modified generalized Chaplygin gas as a dark energy fluid (exotic matter) present in the thin layer of matter-shell. The stability of these constructed thin-shell wormholes is investigated in the scenario of linear perturbations. We conclude that static stable as well as unstable configurations are possible for cylindrical thin-shell wormholes.
In this article we study the mechanical stability of spherically symmetric thin shells with charge, in Einstein-Maxwell and Einstein-Born-Infeld theories. We analyze linearized perturbations preserving the symmetry, for shells around vacuum and shells surrounding non charged black holes.
This paper investigates the dynamics of thin-shell in the presence of perfect fluid as well as the scalar field. We formulate the equations of motion using Israel thin-shell formalism by taking the interior and exterior regions of Schwarzschild, Kerr as well as Kerr-Newmann black hole. We find numerical solutions of equations of motion and effective potential to analyze the scalar shell for collapse and expansion. It is found that the rate of collapse and expansion of scalar shell through shell's radius depends on charge and rotation parameters. We conclude that the massive scalar shell leads …
Using 'Cut and Paste' technique, we develop a thin shell wormhole in heterotic string theory. We determine the surface stresses, which are localized in the shell, by using Darmois-Israel formalism. The linearized stability of this thin wormhole is also analyzed.
We provide a new type of thin-shell wormhole from the black holes with dilaton and monopole fields. The dilaton and monopole that built the black holes may supply fuel to construct the wormholes. Several characteristics of this thin-shell wormhole have been discussed. Finally, we discuss the stability of the thin-shell wormholes with a "phantom-like" equation of state for the exotic matter at the throat.
By applying 'Darmois-Israel formalism', we establish a new class of thin shell wormhole in the context of global monopole resulting from the breaking of a global O(3) symmetry. Since global monopole is asymptotically conical (no longer asymptotically flat), we call it as conical thin shell wormhole. Different characteristics of this conical thin shell wormhole, namely, time evolution of the throat, stability, total amount of exotic matter have been discussed.
In the case of crossing thin dust shells the momentum conservation law is found. For two crossing isotropic shells it coincides with the 't Hooft-Dray formula. The system of one isotropic and one time-like shell is considered. In this case we found a very simple formula which relate velocities of dust shell before and after crossing.
A thin-shell wormhole is theoretically constructible by surgically grafting together two Schwarzschild spacetimes using the so-called cut-and-paste technique. By describing such a wormhole as the limiting case of a spherical shell, it is shown that the structure must be unstable to linearized radial perturbations. Some earlier studies by the author et al. have shown, however, that under certain conditions, thin-shell wormholes can be stable.
The thermodynamic stability of a thin-shell wormhole in a Schwarzschild bulk is considered. From the first law, entropy function is found which satisfies the local intrinsic stability conditions. Heat capacity emerges as a well-defined regular function justifying the stability of a Schwarzschild thin-shell wormhole. The scope of applications of the method is not limited by the Schwarzschild wormhole.
Previous analysis about thin-shell wormholes associated to cosmic strings are extended. More evidence is found supporting the conjecture that, under reasonable assumptions about the equations of state of matter on the shell, the configurations are not stable under radial velocity perturbations.
We study spherically symmetric timelike thin-shells in $3+1-$dimensional bulk spacetime with a variable equation of state for the fluid presented on the shell. In such a fluid the angular pressure $p$ is a function of both surface energy density $σ$ and the radius $R$ of the thin-shell. Explicit cases of the thin shells connecting two non-identical cloud of strings spacetimes and a flat Minkowski spacetime to the Schwarzschild metric are investigated.
A concentric charged thin-shell encircling a Reissner-Nordström black hole screens the clectric / magnetic charge completely to match with an external Schwarzschild black hole. The negative mass thin-shell is shown to be stable against radial perturbations. It is shown further that by reversing the roles of inside Reissner-Nordström and outside Schwarzschild geometries the mass of the appropriate shell becomes positive.
A spherical planetary nebula is described as a geometric model. The nebula itself is considered as a thin-shell which visualized as a boundary of two spacetimes. The inner and outer curvature tensors of the thin-shell are found in order to get an expression of the energy-momentum tensor on the thin-shell. The energy density and pressure expressions are derived using the energy-momentum tensor. The time evolution of the radius of the thin-shell is obtained in terms of the energy density. The model is tested by using a simple power function for decreasing energy density and the evolution pattern…
In this paper, we apply the cut and paste procedure to charged black string for the construction of thin-shell wormhole. We consider the Darmois-Israel formalism to determine the surface stresses of the shell. We take Chaplygin gas to deal with the matter distribution on shell. The radial perturbation approach (preserving the symmetry) is used to investigate the stability of static solutions. We conclude that stable static solutions exist both for uncharged and charged black string thin-shell wormholes for particular values of the parameters.
We investigate the thin-shell wormholes constrained by cosmological observations for the first time in the literature. Without loss of generality, we study the thin-shell wormholes in $ω$CDM model and analyze their stability under perturbations preserving the symmetry. Firstly, we constrain the $ω$CDM model using a combination of Union 2.1 SNe Ia data, the latest $H(z)$ data and CMB data. Secondly, we use the constrained dark energy equation of state (EoS) $ω$ which lies in $[-1.05,-0.89]$ to investigate thin-shell wormholes of various black hole spacetimes. We find that the stable Schwarzschi…
We analytically explore the effect of falling matter on a spherically symmetric wormhole supported by a spherical shell composed of exotic matter located at its throat. The falling matter is assumed to be also a thin spherical shell concentric with the shell supporting the wormhole, and its self-gravity is completely taken into account. We treat these spherical thin shells by Israel's formalism of metric junction. When the falling spherical shell goes through the wormhole, it necessarily collides with the shell supporting the wormhole. To treat this collision, we assume the interaction between…
Recent studies relating the approximations for the equations of state for thin shells and their consequent perturbative evolution are extended to thin-shell wormholes in theories beyond general relativity and more than four spacetime dimensions. The assumption of equations of state of the same form for static and slowly evolving shells appears as a strong restriction excluding the possibility of oscillatory evolutions. Then the new results considerably differ from previous ones obtained within the usual linearized approach.
Mazharimousavi and Halilsoy [1] recently proposed wormhole solutions in $f(R)$-gravity that satisfy energy conditions but are unstable. We show here that stability could still be achieved for thin-shell wormholes obtained by gluing the wormholes in $f(R)$-gravity with the exterior Schwarzschild vacuum. Using the new geometrical constraints from thin-shell "mass" and from external "force" developed by Garcia, Lobo and Visser, we demarcate and analyze the stability regions.
It is shown in this paper that thin-shell wormholes, mathematically constructed by the standard cut-and-paste technique, can, under fairly general conditions, be compatible with quantum field theory.
In this article, we consider spherical thin shells of matter surrounding black holes in F(R) theories of gravity. We study the stability of the static configurations under perturbations that conserve the symmetry. In particular, we analyze the case of charged shells outside the horizon of non--charged black holes. We obtain that stable static thin shells are possible if the values of the parameters of the model are properly selected.
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…
We study the problem of quantization of thin shells in a Weyl-Dirac theory by deriving a Wheeler-DeWitt equation from the dynamics. Solutions are found which have interpretations in both cosmology and particle physics.
This paper discusses the theoretical construction of thin-shell wormholes from Kiselev black holes. We assume a barotropic equation of state for the exotic matter on the shell. While most of these wormholes are unstable to linearized radial perturbations, a limit argument is used to show that under certain conditions, stable solutions can be found.
We revisit the stability analysis of cylindrical thin shell wormholes which have been studied in literature so far. Our approach is more systematic and in parallel to the method which is used in spherically symmetric thin shell wormholes. The stability condition is summarized as the positivity of the second derivative of an effective potential at the equilibrium radius, i.e. $V^{\prime \prime}\left(a_{0}\right) >0$. This may serve as the master equation in all stability problems for the cylindrical thin-shell wormholes.
We introduce two classes of spherically symmetric spacetimes having a thin shell of matter, in non-quadratic F(R) theories of gravity with non-constant scalar curvature R. In the first, the thin shell joins an inner region with an outer one, while in the second it corresponds to the throat of a wormhole. In both scenarios, we analyze the stability of the static configurations under radial perturbations. As particular examples in spacetimes with a cosmological constant, we present charged thin shells surrounding a non-charged black hole and charged thin-shell wormholes. We show that in both cas…
Starting from Israel equations for the spherically symmetric thin shells we introduce the effective potential and show how it can be used in constructing, without further thorough investigation, the corresponding Carter-Penrose diagrams describing clearly the global geometry of the composite space-time manifolds. We demonstrate, how this new method works, by considering all possible configurations for the neutral thin dust shell immersed into different types of Reissner-Nordström electro-vacuum manifolds.
In this paper we consider some applications of the extended Dray-t'Hooft-Redmount relation. In particular, using this relation, we study geometries of interacting thin shells near the future Cauchy horizon of a Reissner-Nordstrom black hole.
Asymmetric thin-shell wormholes from two traversable Morris-Thorne wormhole spacetimes, with identical shape but different redshift functions, are constructed. Energy density of the thin-shell wormhole derives its power from a Morris-Thorne wormhole which is already exotic. By choice, the weak energy condition for the thin-shell wormhole is satisfied. A linear barotropic equation of state is assumed to hold after the radial perturbations. The fate of our thin-shell wormhole, after the perturbation, is striking: the asymmetric thin-shell wormhole is destined either to collapse to the original M…
We construct the solutions of slowly rotating gravastars with a thin shell. In the zero-rotation limit, we consider the gravastar composed of a de Sitter core, a thin shell, and Schwarzschild exterior spacetime. The rotational effects are treated as small axisymmetric and stationary perturbations. The perturbed internal and external spacetimes are matched with a uniformly rotating thin shell. We assume that the angular velocity of the thin shell, $Ω$, is much smaller than the Keplerian frequency of the nonrotating gravastar, $Ω_k$. The solutions within an accuracy up to the second order of $Ω/…
This paper develops a new solution of gravitational vacuum star in the background of charged Kiselev black holes as an exterior manifold. We explore physical features and stability of thin-shell gravastars with radial perturbation. The matter thin layer located at thin-shell greatly affects stable configuration of the developed structure. We assume three different choices of matter distribution such as barotropic, generalized Chaplygin gas and generalized phantomlike equation of state. The last two models depend on the shell radius, also known as variable equation of state. For barotropic mode…
Abstract This short paper investigates the harmonic behavior of a general-relativistic thin-shell wormhole supported by a particular type of exotic fluid. The exotic fluid obeys a never-studied-before metric-dependent equation of state. This equation of state is tailored such that the wormhole's throat undergoes a harmonic-like behavior before damping to an equilibrium radius. Eventually, the mirror-symmetric Schwarzschild thin-shell wormhole is studied in this framework as an example.
We reconsider the generalized flare-out conditions in static wormhole throats given by Hochberg and Visser. We show that due to the presence of matter sources on the throat, these conditions are not applicable to the thin-shell wormholes.
We construct a new type of thin-shell wormhole for non-asymptotically flat charged black holes in generalized dilaton-axion gravity inspired by low-energy string theory using cut-and-paste technique. We have shown that this thin shell wormhole is stable. The most striking feature of our model is that the total amount of exotic matter needed to support the wormhole can be reduced as desired with the suitable choice of the value of a parameter. Various other aspects of thin-shell wormhole are also analyzed.
We obtain rotating solutions of regular black holes which are constructed of de Sitter spacetime with the axisymmetric stationary perturbation within the timelike charged thin shell and the Kerr-Newman geometry with sufficiently small rotation outside the shell. To treat the slowly rotating thin shell, we employ the method developed by de la Cruz and Israel. The thin shell is assumed to be composed of a dust in the zero-rotation limit and located inside the inner horizon of the black hole solution. We expand the perturbation in powers of the rotation parameter of the Kerr-Newman metric up to t…
We study thin shells of matter in (2+1)-dimensional F(R) theories of gravity with constant scalar curvature R. We consider a wide class of spacetimes with circular symmetry, in which a thin shell joins an inner region with an outer one. We analyze the stability of the static configurations under radial perturbations. As examples of spacetimes asymptotically anti-de Sitter, we present a charged bubble and a charged thin shell surrounding a non-charged black hole. In both cases, we show that stable solutions can be found for suitable values of the parameters.
We prove the impossibility of cylindrical thin-shell wormholes supported by matter satisfying the energy conditions everywhere, under reasonable assumptions about the asymptotic behaviour of the - in general different - metrics at each side of the throat. In particular, we reproduce for singular sources previous results corresponding to flat and conical asymptotics, and extend them to a more general asymptotic behaviour. Besides, we establish necessary conditions for the possibility of non exotic cylindrical thin-shell wormholes.
In this article, we study thin shells of matter connecting charged black string geometries with different values of the corresponding parameters. We analyze the matter content and the mechanical stability of the shells undergoing perturbations that preserve the cylindrical symmetry. Two different global configurations are considered: an interior geometry connected to an exterior one at the surface where the shell is placed, and two exterior geometries connected by a wormhole throat located at the shell position.
Interaction / collision of two concentric spherical thin-shells of linear fluid resulting in collapse has been considered recently. We show that addition of finely tuned electric charges on the shells apart from the cosmological constant serves to delay the collapse indefinitely, yielding an ever colliding system of two concentric fluid shells. Given the finely tuned charges this provides an example of a perpetual two-body motion in general relativity.
Recently, Bañados, Teitelboim and Zanelli (BTZ) \cite{BTZ1992} has discovered an explicit vacuum solution of (2+1)-dimensional gravity with negative cosmological constant. It has been argued that the existence of such physical systems with an event horizon and thermodynamic properties similar to (3+1) dimensional black holes. These vacuum solutions of (2+1)-dimensional gravity are asymptotically anti-de Sitter and are known as BTZ black holes. We provide a new type of thin-shell stable wormhole from the BTZ black holes. This is the first example of stable thin shell wormhole in (2+1)-dimension…
To explain Gamma Ray Bursts, Ruffini argued that the event horizon of a charged black hole is surrounded by a special region called, the Dyadosphere where electric field exceeds the critical value for $e^+$ $e^-$ pair production. In the present work, we construct a thin shell wormhole by performing a thought surgery between two dadospheres. Several physical properties of this thin shell wormhole have been analyzed.
The characterization and mechanical stability of charged thin shells with spherical symmetry are analyzed in the context of Einstein-Born-Infeld theory. The study of stability is performed by considering linearized perturbations preserving the symmetry of the static configurations. It is found that as the charge increases, the shells can be stable for a wider range of the parameters.
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 construct a broad family of thin-shell wormholes with circular symmetry in (2+1)-dimensional F(R) theories of gravity, with constant scalar curvature R. We study the stability of the static configurations under perturbations preserving the symmetry. We present charged thin-shell wormholes as examples of spacetimes with a negative cosmological constant. We show that stable solutions are possible when suitable values of the parameters are taken.
In this paper we construct charged thin-shell wormholes in (2+1)-dimensions applying the cut-and -paste technique implemented by Visser, from a BTZ black hole which was discovered by Banados, Teitelboim and Zanelli, and the surface stress are determined using the Darmois-Israel formalism at the wormhole throat. We analyzed the stability of the shell considering phantom-energy or generalised Chaplygin gas equation of state for the exotic matter at the throat. We also discussed the linearized stability of charged thin-shell wormholes around the static solution.
We show that the cold horizon of the extremal Reissner-Nordström can be considered as the throat of a thin-shell wormhole with zero total exotic matter and positive angular pressure. Such a wormhole is physical and stable against radial perturbations provided an appropriate perfect fluid exists at the throat.
This paper discusses a new type of thin-shell wormhole constructed by applying the cut-and-paste technique to two copies of a charged black hole in generalized dilaton-axion gravity, which was inspired by low-energy string theory. After analyzing various aspects of this thin-shell wormhole, we discuss its stability to linearized spherically symmetric perturbations.
The role of angular momentum in a 2+1-dimensional rotating thin-shell wormhole (TSW) is considered. Particular emphasis is made on stability when the shells (rings) are counterrotating. We find that counter-rotating halves make the TSW supported by the equation of state of a linear gas more stable. Under a small velocity dependent perturbation, however, it becomes unstable.
In this paper, we construct thin-shell wormholes by applying the cut and paste procedure to a regular charged black hole in nonlinear electrodynamics field. We discuss different physical aspects of wormholes such as, the possible equation of state to matter shell, attractive or repulsive nature of wormhole and total amount of exotic matter required. The thin-shell equation of motion with and without cosmological constant is also investigated under linearized perturbation. Finally, we explore the stability regions interpreted by the parameter $β$ (speed of sound) and conclude that there are rea…
We investigate a new thin-shell wormhole constructed by surgically grafting two regular charged black holes arising from the action using nonlinear electrodynamics coupled to general relativity. The stress-energy components within the shell violate the null and weak energy conditions but obey the strong energy condition. We study the stability in two ways: (i) taking a specific equation of state at the throat and (ii) analyzing the stability to linearized spherically symmetric perturbations about a static equilibrium solution. Various other aspects of this thin-shell wormhole are also analyzed…
We cut and paste two Banados-Teitelboim-Zanelli (BTZ) spacetimes at a throat by the Darmois-Israel method to construct a rotating wormhole with a thin shell filled with a barotropic fluid. The thin shell at the throat and both sides of the throat corotate. We investigate the linear stability of the thin shell of the rotating wormhole against radial perturbations. We show that the wormhole becomes more and more stable the larger its angular momentum is until the angular momentum reaches a critical value and that the behavior of a condition for stability significantly changes when the angular mo…
We study the massive scalar field of a charged particle held at rest in conical thin-shell spacetimes with one or two asymptotic regions. Resonant and stable scalar Green's functions are characterized in terms of the coupling of the field to the trace of the extrinsic curvature jump at the shell. Stable coupling values, within the safety domain of the configuration parameters, are used to analyze the self-force of static point charges.
We study the stability of thin-shell wormholes in Einstein-Maxwell-Gauss-Bonnet gravity. The equation of state of the thin shell wormhole is considered first to obey a generalized Chaplygin gas and then we generalize it to an arbitrary state function which covers all known cases studied so far. In particular we study the modified Chaplygin gas and give an assessment for a general parotropic fluid. Our study is in d-dimensions and with numerical analysis in d=5 we show the effect of the GB parameter in the stability of thin-shell wormholes against the radial perturbations.
