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.     

Higher Dimensional Spherically Symmetric Expanding Wormholes in Einstein’s Gravity

We present (n+1)-dimensional expanding structures in a cosmological background. Due to the expansion of spacetime the throat of wormholes enlarge with time. These solutions are examined in the Einstein’s framework. A general linear relation between diagonal elements of an anisotropic energy-momentum tensor is assumed and the spherically symmetric structures are obtained. Solutions include naked singularity and expanding wormholes in an open universe. The traversibility of wormhole solutions is explored and we find that they are basically traversable. Finally, we consider the corresponding energy-momentum tensor properties and specially take into account the standard energy conditions.     

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.     

Entropic force, holography and thermodynamics for static space-times

Recently Verlinde has suggested a new approach to gravity which interprets gravitational interaction as a kind of entropic force. The new approach uses the holographic principle by stating that the information is kept on the holographic screens which coincide with equipotential surfaces. Motivated by this new interpretation of gravity (but not being limited by it) we study equipotential surfaces, the Unruh–Verlinde temperature, energy and acceleration for various static space-times: generic spherically symmetric solutions, axially symmetric black holes immersed in a magnetic field, traversable spherically symmetric wormholes of an arbitrary shape function, system of two and more extremely charged black holes in equilibrium. In particular, we have shown that the Unruh–Verlinde temperature of the holographic screen reaches absolute zero on the wormhole throat independently of the particular form of the wormhole solution.     

Noether symmetries in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">G</Emphasis>) gravity

We explore Noether symmetries of the Friedmann–Robertson–Walker universe model in modified Gauss–Bonnet gravity for both vacuum and nonvacuum (dust fluid) cases. We evaluate symmetry generators and the corresponding conserved quantities by using separation of variables and a power-law form. We construct exact f(G) models and study accelerating expansion of the universe in terms of a scale factor, deceleration, and the EoS parameters. We also check the validity of energy conditions through the weak energy conditions for our constructed model. The state finder parameters indicate the resemblance of our constructed models to the ΛCDM model. We conclude that our results are consistent with the recent astrophysical observations.     

Curved traversable wormholes in (3+1)-dimensional spacetime

We present the general method of constructing curved traversable wormholes in (3+1)-d spacetime and proceed to thoroughly discuss the physics of a zero tidal force metric without cross-terms. The (3+1)-d solution is compared with the recently studied lower-dimensional counterpart, where we identify that the much richer physics—involving pressures and shear forces of the mass-energy fluid supporting the former—is attributed to the mixing of all three spatial coordinates. Our (3+1)-d universe is the lowest dimension where such nontrivial terms appear. An explicit example, the static zero tidal force (3+1)-d catenary wormhole is analysed and we show the existence of a geodesic through it supported locally by non-exotic matter, similar to the (2+1)-d version. A key difference is that positive mass-energy is used to support the entire (3+1)-d catenary wormhole, though violation of the null energy condition in certain regions is inevitable. This general approach of first constructing the geometry of the spacetime and then using the field equations to determine the physics to support it has the potential to discover new solutions in general relativity or to generalise existing ones. For instance, the metric of a time-evolving inflationary wormhole with a conformal factor can actually be geometrically constructed using our method.     

Gravitational Lensing by Traversable Wormholes Supported by Three-Form Fields

In this paper, the deflection angle of light by traversable wormholes, which are supported by the three-form fields, are studied. The specific forms of the redshift and shape functions that produce results compatible with the energy conditions at throat of the wormholes are used. Having used the well-defined parameter sets of the three-form wormholes, the photon geodesic motion is investigated under the effective potential of the wormhole background. As a result, it is discovered that the radius of the photon sphere can be used to analyze the geometrical structures of a physical wormhole. The analytical form of the effective potential is used to figure out a deflection angle of light caused by wormholes with the three-from fields. In this work, the relativistic images generated from the wormholes are also constructed.     

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.     

Self-accelerated Universe Induced by Repulsive Effects as an Alternative to Dark Energy and Modified Gravities

The existence of current–time universe’s acceleration is usually modeled by means of two main strategies. The first makes use of a dark energy barotropic fluid entering by hand the energy–momentum tensor of Einstein’s theory. The second lies on extending the Hilbert–Einstein action giving rise to the class of extended theories of gravity. In this work, we propose a third approach, derived as an intrinsic geometrical effect of space–time, which provides repulsive regions under certain circumstances. We demonstrate that the effects of repulsive gravity naturally emerge in the field of a homogeneous and isotropic universe. To this end, we use an invariant definition of repulsive gravity based upon the behavior of the curvature eigenvalues. Moreover, we show that repulsive gravity counterbalances the standard gravitational attraction influencing both late and early times of the universe evolution. This phenomenon leads to the present speed up and to the fast expansion due to the inflationary epoch. In so doing, we are able to unify both dark energy and inflation in a single scheme, showing that the universe changes its dynamics when \({\ddot{H}\over H}=-2 \dot{H}\), at the repulsion onset time where this condition is satisfied. Further, we argue that the spatial scalar curvature can be taken as vanishing because it does not affect at all the emergence of repulsive gravity. We check the goodness of our approach through two cosmological fits involving the most recent union 2.1 supernova compilation.     

<Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity constraints from gravitational waves

The recent LIGO observation sparked interest in the field of gravitational wave signals. Besides the gravitational wave observation the LIGO collaboration used the inspiraling black hole pair to constrain the graviton mass. Unlike general relativity, f(R) theories have a characteristic non-zero mass graviton. We apply this constraint on the graviton mass to viable f(R) models in order to find the effects on model parameters. We find it possible to constrain the parameter space with these gravity wave based observations. We consider the popular Hu–Sawicki model as a case study and find an appropriate parameter bracket. The result generalizes to other f(R) theories and can be used to constrain the parameter space.     

Do universes with parallel cosmic strings or two-dimensional wormholes have closed timelike curves?

Regions of empty spacetime with one translation symmetry and no gravitational waves can be examined with the equations of 2+1 gravity. Such regions are locally Minkowskian but may include parallel cosmic strings or wormholes that extend to infinity in the third space dimension. The time evolution problem is set in the framework of a recent constrained Hamiltonian formulation for 2+1 gravity. A wormhole developes closed timelike curves in a finite amount of time for roughly half of all possible initial conditions. A pair of cosmic strings with relative angular momentum, unlike a spinning string, does not have closed timelike curves.     

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.     

Wormhole solutions in Gauss–Bonnet–Born–Infeld gravity

A new class of solutions which yields an (n + 1)-dimensional spacetime with a longitudinal nonlinear magnetic field is introduced. These spacetimes have no curvature singularity and no horizon, and the magnetic field is non singular in the whole spacetime. They may be interpreted as traversable wormholes which could be supported by matter not violating the weak energy conditions. We generalize this class of solutions to the case of rotating solutions and show that the rotating wormhole solutions have a net electric charge which is proportional to the magnitude of the rotation parameter, while the static wormhole has no net electric charge. Finally, we use the counterterm method and compute the conserved quantities of these spacetimes.     

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.     

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.     

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.     

Exact solutions and conserved quantities in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) Gravity

This paper explores Noether and Noether gauge symmetries of anisotropic universe model in f(R, T) gravity. We consider two particular models of this gravity and evaluate their symmetry generators as well as associated conserved quantities. We also find exact solution by using cyclic variable and investigate its behavior via cosmological parameters. The behavior of cosmological parameters turns out to be consistent with recent observations which indicates accelerated expansion of the universe. Next we study Noether gauge symmetry and corresponding conserved quantities for both isotropic and anisotropic universe models. We conclude that symmetry generators and the associated conserved quantities appear in all cases.     

<Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity solutions for evolving wormholes

The scalar–tensor f(R) theory of gravity is considered in the framework of a simple inhomogeneous space-time model. In this research we use the reconstruction technique to look for possible evolving wormhole solutions within viable f(R) gravity formalism. These f(R) models are then constrained so that they are consistent with existing experimental data. Energy conditions related to the matter threading the wormhole are analyzed graphically and are in general found to obey the null energy conditions (NEC) in regions around the throat, while in the limit \(f(R)=R,\) NEC can be violated at large in regions around the throat.