We construct an asymptotically flat Morris-Thorne wormhole solution supported by anisotropic matter fluid and a vector field which is coupled to gravity in a non-minimal way with broken Abelian gauge symmetry. In this paper, a specific shape function is considered. We find that the ansatz of vector field plays a significant role in determining the spacetime geometry of the wormhole. If there exists the electrostatic potential only, the redshift function could be considered as a constant value, implying the vanishing tidal force. However, when the vector potential in radial-direction is involved, the r-component of extended Maxwell equations at the wormhole's throat is invalid. To solve this issue, a thin shell is introduced near the throat, dividing the spacetime into two parts. Furthermore, it is proved that the spacetime geometry of wormhole could be smooth at junction position if the expressions of redshift function and vector potential are given appropriately. Finally, the energy conditions and the volume integral quantifer are explored.
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…
The gravitational perturbation of the Morris-Thorne wormhole has been derived by using the Newman-Penrose formalism. We apply Teukolsky equation to the wormhole spacetime, compute the perturbed Weyl scalars, $Ψ_{4}^{(1)}$ and obtain its master equation, decomposed in spin weighted spherical harmonics with spin weight $-2$. For simplicity, we consider the perturbation provoked by a single gaussian pulse of pressureless dust matter.
Two critical issues in the study of Morris-Thorne wormholes concerns the stability of such structures, as well as their compatibility with quantum field theory. This note discusses an important subset characterized by zero tidal forces. It is shown that such wormholes (1) are in stable equilibrium using a criterion based on the Tolman-Oppenheimer-Volkoff (TOV) equation and (2) are not in direct conflict with quantum field theory.
It is well known that phantom energy, which is characterized by the equation of state $p=ωρ$, $ω<-1$, can support Morris-Thorne wormholes since it leads to a violation of the null energy condition. The purpose of this note is to show that the converse is also true in the following sense: for a typical shape function, the equation of state of exotic matter in the vicinity of the throat is given by $p_r=ωρ$, $ω<-1$, where $p_r$ is the radial pressure. Some implications thereof are also considered.
Morris-Thorne wormholes in static pseudo-spherically symmetric spacetimes
本文研究了具有伪球对称性的经典广义相对论静态虫孔位形。我们表明，除了Lobo和Mimoso在参考物理中讨论的双曲虫孔解之外，修订版本\ D { \bf 82}，044034（2010），存在另一种虫孔类，其是球形Morris-Thorne虫孔的真正伪球形对应物（与Lobo-Mimoso虫孔类相反），因为满足了最初由Morris和Thorne为球对称虫孔定义的所有约束。我们发现，对于这两类双曲虫孔的能量密度，在喉，总是负的，而径向压力是积极的，相反的球对称的莫里斯-索恩虫孔。具体的双曲虫孔的构造和讨论施加不同的条件的径向和侧向压力，或通过考虑有限的选择的红移和形状函数。特别是，我们表明，双曲虫洞不能持续在喉部的幻影能量，并有伪球对称的虫洞支持的物质与各向同性的压力，其特征在于空间部分的角度赤字（或过剩）。
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…
In the context of $2+1-$dimensional gravity coupled to a particular nonlinear electrodynamics (NED), we obtain a class of traversable / Morris-Thorne type wormhole solutions. The problem is reduced to a single function dependence in which the shape function acts as generator to the wormholes. The field ansatz is pure magnetic and the nonlinear Lagrangian is $\sqrt{F_{μν}F^{μν}}$ i.e. the square root of the Maxwell Lagrangian. In $2+1-$dimensions the source-free pure magnetic non-linear Maxwell equation with square-root Lagrangian is trivially satisfied. The exotic energy density is found expli…
It is well known that a Morris-Thorne wormhole can only be held open by violating the null energy condition, physically realizable by the use of "exotic matter." Unfortunately, even a small or moderately-sized wormhole would have a radial tension equal to that of the interior of a massive neutron star. So outside a neutron-star setting, such an outcome is problematical at best, calling for more than an appeal to exotic matter whose introduction had a completely different objective and with possibly different outcomes. The purpose of this paper is to account for the enormous radial tension in t…
In this study, we reach the equations of motion of Morris-Thorne wormhole geometry by means of the Einstein Field Equations and Klein-Gordon Equation of Scalar-Tensor theory by direct calculation. We discuss the anisotropic matter energy distribution. We determine a relation between the radial and the transverse pressures. Hence, we express the anisotropic energy momentum tensor in terms of one pressure class, by means of that relation. Besides that, we check the isotropic case and show that there is no traversable wormhole, in the zero redshift function situation, if the space is fulfilled wi…
In this paper we have established an asymptotically conical Morris-Thorne wormhole solution supported by anisotropic matter fluid and a global monopole charge in the framework of a $1+3$ dimensional gravity minimally coupled to a triplet of scalar fields $ϕ^a$, resulting from the breaking of a global $O(3)$ symmetry. For the anisotropic matter fluid we have considered the equation of state (EoS) given by $\mathcal{P}_r=ωρ$, with a consequence $ω<-1$, implying a so-called phantom energy at the throat of the wormhole which violates the energy conditions. In addition, we study the weak gravitatio…
We study static traversable wormholes obtained by Morris and Thorne in general relativity (GR) in the framework of a modified theory of gravity. The modified gravitational action $f(R,T)$ is a function of the Ricci scalar ($R$) and of the trace of the energy momentum tensor ($T$). For a modified gravity $f(R,T)=R+αR^{2}+λT$, where $α$ and $λ$ are constants, we obtain wormhole solutions (WH) with normal matter for a relevant shape functions. The energy conditions are checked at the throat and away from the throat of the WH. The coupling parameters $α$ and $λ$ in the gravitational action play an…
We consider the wormhole of Ellis, Bronnikov, Morris and Thorne (EBMT), arising from Einstein's equations in presence of a phantom scalar field. In this paper we propose a simplified derivation of the linear instability of this system, making comparisons with previous works on this subject (and generalizations) by Gonzalez, Guzman, Sarbach, Bronnikov, Fabris and Zhidenko.
Stress-energy tensor of quantized scalar fields in a zero-tidal wormhole
School of Physics and Optoelectronics, South China University of Technology（华南理工大学物理与光电工程学院）；Faculty of Arts and Sciences, Beijing Normal University, Zhuhai（北京师范大学珠海校区文理学院）
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…
Wormhole solutions in classical General Relativity are unstable and hence non traversable. Morris and Thorne discovered a traversable wormhole solution that required the energy momentum tensor of matter sources to violate various energy conditions and are out of the purview of the standard model of particle physics. The search for traversable wormhole solutions in Modified Theories of Gravity has been of significant interest in the decades after Morris and Thorne first published their results as such violations may be avoided in such theories. This work comprehensively reviews traversable worm…
In this work, wormholes, tunnel like structures introduced by Morris \& Thorne \cite{Morris95}, are explored within the framework of $f(R)$ gravity. Using the shape function $b(r)=r_0\big(\frac{r}{r_0}\big)^γ$, where $0<γ<1$, and the equation of state $p_r=ωρ$, the $f(R)$ function is derived and the field equations are solved. Then null, weak, strong and dominated energy conditions are analyzed and spherical regions satisfying these energy conditions are determined. Furthermore, we calculated the range of the radius of the throat of the wormhole, where the energy conditions are satisfied.
Morris \& Thorne \cite{morris1} proposed geometrical objects called traversable wormholes that act as bridges in connecting two spacetimes or two different points of the same spacetime. The geometrical properties of these wormholes depend upon the choice of the shape function. In literature, these are studied in modified gravities for different types of shape functions. In this paper, the traversable wormholes having shape function $b(r)=\frac{r_0\tanh(r)}{\tanh(r_0)}$ are explored in $f(R)$ gravity with $f(R)=R+αR^m-βR^{-n}$, where $α$, $β$, $m$ and $n$ are real constants. For different value…
In this work we consider a Generalized Bronnikov-Ellis wormhole and the tideless Morris-Thorne wormhole and we study the propagation of massive scalar fields. We calculate the quasinormal frequencies using the WKB method and the pseudospectal Chebyshev method and we show the presence of an anomalous decay rate for the quasinormal modes in the Generalized Bronnikov-Ellis wormhole. However, such anomalous behaviour is avoided for the fundamental mode in the Morris-Thorne wormhole background.
Morris and Thorne \cite{morris1} proposed traversable wormholes, hypothetical connecting tools, using the concept of Einstein's general theory of relativity. In this paper, the modification of general relativity (in particular $f(R,T)$ theory of gravity defined by Harko et al. \cite{harko}) is considered, to study the traversable wormhole solutions. The function $f(R,T)$ is considered as $f(R,T)=R+αR^2+βT$, where $α$ and $β$ are controlling parameters. The shape and red shift functions appearing in the metric of wormhole structure have significant contribution in the development of wormhole so…
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.
Here we shall show how to reconstruct the shape function of a spherically symmetric traversable Lorenzian wormhole near its throat if one knows high frequency quasinormal modes of the wormhole. The wormhole spacetime is given by the Morris-Thorne ansatz. The solution to the inverse problem via fitting of the parameters within the WKB approach is unique for arbitrary tideless wormholes and some wormholes with non-zero tidal effects, but this is not so for arbitrary wormholes. As examples, we reproduce the near throat geometries of the Bronnikov-Ellis and tideless Morris-Thorne metrics by their …
The strategy adopted in the original Morris-Thorne wormhole was to retain complete control over the geometry at the expense of certain engineering considerations. The purpose of this paper is to obtain several complete wormhole solutions by assuming a noncommutative-geometry background with a concomitant isotropic-pressure condition. This condition allows us to consider a cosmological setting with a perfect-fluid equation of state. An extended form of the equation generalizes the first solution and subsequently leads to the generalized Chaplygin-gas model and hence to a third solution. The sol…
We study the absorption of massless scalar waves in a geometry that interpolates between the Schwarzschild solution and a wormhole that belongs to the Morris-Thorne class of solutions. In the middle of the interpolation branch, this geometry describes a regular black hole. We use the partial wave approach to compute the scalar absorption cross section in this geometry. Our results show that black holes and wormholes present distinctive absorption spectra. We conclude, for instance, that the wormhole results are characterized by the existence of quasibound states which generate Breit-Wigner-lik…
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…
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…
When Morris and Thorne first proposed the possible existence of traversable wormholes, they adopted the following strategy: maintain complete control over the geometry, thereby leaving open the determination of the stress-energy tensor. In this paper we determine this tensor by starting with a noncommutative-geometry background and assuming that the static and spherically symmetric spacetime admits conformal motions. This had been established in a previous collaboration with Rahaman et al. using a slightly different approach. Accordingly, the main purpose of this paper is to show that the worm…
A fundamental property of Morris-Thorne wormholes is the so-called flare-out condition that automatically results in a violation of the null energy condition (NEC) in classical general relativity. By contrast, in $f(R)$ modified gravity, the material threading the wormhole may actually satisfy the NEC, while, at the same time, the effective stress-energy tensor arising from the modified theory violates the NEC, thereby sustaining the wormhole. It is shown in this paper that noncommutative geometry, an offshoot of string theory, can be viewed as a special case of $f(R)$ gravity and can therefor…
