Gravitational Microlensing by Ellis Wormhole: Second Order Effects

Gravitational lensing is the effect of light bending in a gravitational field. It can be used as a possible observational method to detect or exclude the existence of wormholes. In this work, we extend the work by Abe on gravitational microlensing by Ellis wormhole by including the second order deflection term. Using the lens equation and definition of Einstein radius, we find the angular locations of the physical image inside and outside Einstein ring. The work contains a comparative analysis of light curves between the Schwarzschild black hole and the Ellis wormhole that can be used to distinguish such objects though such distinctions are too minute to be observable even in the near future. We also tabulate the optical depth and event rate for lensing by bulge and Large Magellanic Cloud (LMC) stars.     

Thin-Shell Wormholes from Black Holes with Dilaton and Monopole Fields

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.     

Graphene wormholes: A condensed matter illustration of Dirac fermions in curved space

We study the properties of graphene wormholes in which a short nanotube acts as a bridge between two graphene sheets, where the honeycomb carbon lattice is curved from the presence of 12 heptagonal defects. By taking the nanotube bridge with very small length compared to the radius, we develop an effective theory of Dirac fermions to account for the low-energy electronic properties of the wormholes in the continuum limit, where the frustration induced by the heptagonal defects is mimicked by a line of fictitious gauge flux attached to each of them. We find in particular that, when the effective gauge flux from the topological defects becomes maximal, the zero-energy modes of the Dirac equation can be arranged into two triplets, that can be thought as the counterpart of the two triplets of zero modes that arise in the dual instance of the continuum limit of large spherical fullerenes. We further investigate the graphene wormhole spectra by performing a numerical diagonalization of tight-binding Hamiltonians for very large lattices realizing the wormhole geometry. The correspondence between the number of localized electronic states observed in the numerical approach and the effective gauge flux predicted in the continuum limit shows that graphene wormholes can be consistently described by an effective theory of two Dirac fermion fields in the curved geometry of the wormhole, opening the possibility of using real samples of the carbon material as a playground to experiment with the interaction between the background curvature and the Dirac fields.     

Spherically Symmetric Wormhole Gravitational Lens Deflection Angle Signifying Braneworld Cosmology

Previously, the gravitational lens of a wormhole was introduced by various researchers. Their treatment was focused basically on the lens signature that describes wormhole geometrical character such as the differences from a black hole or between any various types of wormhole models. The braneworld scenario provides the idea of spacetime with underlying extra-dimensions. The inclusion of extra-dimensional terms in the lens object spacetime line element will result in some variation in the expression for its gravitational lens deflection angle.Thus in this paper we investigate such variation by deriving this deflection angle expression. As such, this paper not only shows the existence of such variation but also suggests the potential utilization of gravitational lensing to prove the existence of extra dimensions by studying the deflection angle characteristic in accordance with the spacetime expansion rate of the universe.     

Deflection of light by black holes and massless wormholes in massive gravity

Weak gravitational lensing by black holes and wormholes in the context of massive gravity (Bebronne and Tinyakov, JHEP 0904:100, 2009) theory is studied. The particular solution examined is characterized by two integration constants, the mass M and an extra parameter S namely ‘scalar charge’. These black hole reduce to the standard Schwarzschild black hole solutions when the scalar charge is zero and the mass is positive. In addition, a parameter \(\lambda \) in the metric characterizes so-called ‘hair’. The geodesic equations are used to examine the behavior of the deflection angle in four relevant cases of the parameter \(\lambda \). Then, by introducing a simple coordinate transformation \(r^\lambda =S+v^2\) into the black hole metric, we were able to find a massless wormhole solution of Einstein–Rosen (ER) (Einstein and Rosen, Phys Rev 43:73, 1935) type with scalar charge S. The programme is then repeated in terms of the Gauss–Bonnet theorem in the weak field limit after a method is established to deal with the angle of deflection using different domains of integration depending on the parameter \(\lambda \). In particular, we have found new analytical results corresponding to four special cases which generalize the well known deflection angles reported in the literature. Finally, we have established the time delay problem in the spacetime of black holes and wormholes, respectively.     

Can electro-magnetic field,anisotropic source and varying Λ be sufficient to produce wormhole spacetime?

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 conditions out side the wormhole throat. Here violation of energy conditions can be compensated by varying cosmological constant. The important feature of this article is that one can get wormhole structure, at least theoretically, comprising with physically acceptable matters.     

Wormhole supported by dark energy admitting conformal motion

In this article, we study the possibility of sustaining static and spherically symmetric traversable wormhole geometries admitting conformal motion in Einstein gravity, which presents a more systematic approach to search a relation between matter and geometry. In wormhole physics, the presence of exotic matter is a fundamental ingredient and we show that this exotic source can be dark energy type which support the existence of wormhole spacetimes. In this work we model a wormhole supported by dark energy which admits conformal motion. We also discuss the possibility of the detection of wormholes in the outer regions of galactic halos by means of gravitational lensing. Studies of the total gravitational energy for the exotic matter inside a static wormhole configuration are also performed.     

A general method for constructing curved traversable wormholes in (2+1)-dimensional spacetime

We develop a general method for constructing curved traversable wormholes in (2+1)-dimensional spacetime, by generating surfaces of revolution around smooth curves. Application of this method to a straight line gives the usual spherically symmetric wormholes. The physics behind (2+1)-d curved traversable wormholes is discussed based on solutions to the Einstein field equations when the tidal force is zero. The Einstein field equations are found to reduce to one equation whereby the mass-energy density varies linearly with the Ricci scalar, which signifies that our (2+1)-d curved traversable wormholes are supported by dust of ordinary and exotic matter without radial tension nor lateral pressure. With this, two examples of (2+1)-d curved traversable wormholes: the helical wormhole and the catenary wormhole, are constructed and we show that there exist geodesics through them supported by non-exotic matter. This general method is applicable to our (3+1)-d spacetime.     

Traversable braneworld wormholes supported by astrophysical observations

In this study, we investigate the characteristics and properties of a traversable wormhole constrained by the current astrophysical observations in the framework of modified theories of gravity (MOG). As a concrete case, we study traversable wormhole space–time configurations in the Dvali–Gabadadze–Porrati (DGP) braneworld scenario, which are supported by the effects of the gravity leakage of extra dimensions. We find that the wormhole space–time structure will open in terms of the 2σ confidence level when we utilize the joint constraints supernovae (SNe) Ia + observational Hubble parameter data (OHD) + Planck + gravitational wave (GW) and z < 0:2874. Furthermore, we obtain several model-independent conclusions, such as (i) the exotic matter threading the wormholes can be divided into four classes during the evolutionary processes of the universe based on various energy conditions; (ii) we can offer a strict restriction to the local wormhole space–time structure by using the current astrophysical observations; and (iii) we can clearly identify a physical gravitational resource for the wormholes supported by astrophysical observations, namely the dark energy components of the universe or equivalent space–time curvature effects from MOG. Moreover, we find that the strong energy condition is always violated at low redshifts.     

Wormholes supported by polytropic phantom energy

It is generally agreed that the acceleration of the Universe can best be explained by the presence of dark or phantom energy. The equation of state of the latter shows that the null energy condition is violated. Such a violation is the primary ingredient for sustaining traversable wormholes. This paper discusses wormholes supported by a more general form called polytropic phantom energy. Its equation of state results in significant generalizations of the phantom-energy and, in some cases, the generalized Chaplygin-gas wormhole models, both of which continue to receive considerable attention from researchers. Several specific solutions are explored, namely, a constant redshift function, a particular choice of the shape function, and an isotropic-pressure model with various shape functions. Some of the wormhole spacetimes are asymptotically flat, but most are not.     

A positive cosmological constant in string theory through AdS/CFT wormholes

There are two important examples of physical systems which violate the strong energy condition: Universes (like, it would seem, our own) with a positive cosmological constant, and wormholes. We suggest that a positive cosmological constant can be reconciled with string theory by considering wormholes in string backgrounds. This is argued in two directions: first, we show that brane-worlds with positive cosmological constants give rise to bulk singularities which are best resolved by embedding the brane-world in an AdS/CFT wormhole; and second, for the simplest kind of wormhole in an asymptotically AdS space, we show that the IR stability of the matter needed to keep the wormhole open requires the presence of a brane-world. UV stability conditions then forbid a negative cosmological constant on the brane-world.     

Observational effects in black and white holes (dynamical wormholes)

The models of wormholes with a topology based on a Reissner-Nordström black and white hole are considered. In these models, there are one entrance in one universe (a black hole) and one exit into another universe (a white hole) corresponding to this entrance. The passage of matter through the wormhole in these models is possible only in one direction (from past to future). All models are considered under the assumption of spherical symmetry. It is shown that all models without a throat do not violate the null energy condition. The model of a Reissner-Nordström black hole containing no singularities inside the horizon has been constructed. The trajectories of particles and light rays passing from one universe into another have been constructed for the simplest Reissner-Nordström black and white hole. Distinctive features have been found for the images of objects from another universe observed through such objects. The characteristics of these images are compared with those for ordinary wormholes.     

Reissner–Nordström thin-shell wormholes with generalized cosmic Chaplygin gas

Following Visser’s approach (Visser in Phys. Rev. D 39:3182, 1989; Nucl. Phys. B 328:203, 1989; Lorentzian wormholes. AIP Press, New York, 1996) of cut and paste, we construct Reissner–Nordström thin-shell wormholes by taking the generalized cosmic Chaplygin gas for the exotic matter located at the wormhole throat. The Darmois–Israel conditions are used to determine the dynamical quantities of the system. The viability of the thin-shell wormholes is explored with respect to radial perturbations preserving the spherical symmetry. We find stable as well as unstable Reissner–Nordström thin-shell wormhole solutions depending upon the model parameters. Finally, we compare our results with both generalized and modified Chaplygin gases.     

The null energy condition in wormholes with cosmological constant

Dynamic and static wormhole solutions of Einsteins equations with the cosmological constant are presented. The dynamic solutions can be interpreted as Friedmann–Robertson–Walker models with traversable wormholes. The null energy condition is checked for both dynamic and static wormholes and it is shown explicitly that the cosmological constant modifies the violation of this condition.     

Twists of fate: Can we make traversable wormholes in spacetime?

The scientific reasons for trying to make traversable wormholes are briefly reviewed. Methods for making wormholes employing a Machian transient mass fluctuation are examined. Several problems one might encounter are mentioned. They, however, may just be engineering difficulties. The use of “quantum inequalities” to constrain the existence of negative mass-energy required in wormhole formation is briefly examined. It is argued that quantum inequalities do not prohibit the formation of artificial concentrations of negative mass-energy.     

Nonsymmetric dynamical thin-shell wormhole in Robinson–Trautman class

The thin-shell wormhole created using the Darmois–Israel formalism applied to Robinson–Trautman family of spacetimes is presented. The stress energy tensor created on the throat is interpreted in terms of two dust streams and it is shown that asymptotically this wormhole settles to the Schwarzschild wormhole with a throat located at the position of the horizon. This behavior shows a nonlinear stability (within the Robinson–Trautman class) of this spherically symmetric wormhole. The gravitational radiation emitted by the Robinson–Trautman wormhole during the transition to spherical symmetry is indistinguishable from that of the corresponding black hole Robinson–Trautman spacetime. Subsequently, we show that the higher-dimensional generalization of Robinson–Trautman geometry offers a possibility of constructing wormholes without the need to violate the energy conditions for matter induced on the throat.     

Traversible wormholes in (2 + 1) dimensions

We investigate traversible wormhole solutions to the Einstein field equations in (2 + 1) dimensions. The constraints on the field equations to obtain a wormhole solution are presented and further constraints for traversibility of the wormhole are also given. We show that there is no analog of the (3 + 1)-dimensional Schwarzschild wormhole in (2 + 1) dimensions. For general wormholes, the radial tension and lateral pressure at the throat of the wormhole must be zero, and the energy density must be negative. Two specific wormhole solutions are presented. We perform a stability analysis on the solutions.     

Semi-classical wormholes are unstable

We show that Lorentzian (traversable) wormholes with semi-classical spacetimes are unstable. Semi-classicality of the energy–momentum tensor of the exotic matter used to stabilize the wormhole implies localization of its wavefunction in phase space, leading to evolution according to the classical equations of motion. Previous results related to violation of the NEC then require that the matter is unstable to small perturbations.