It is shown that the existence of static, cylindrically symmetric wormholes does not require violation of the weak or null energy conditions near the throat, and cylindrically symmetric wormhole geometries can appear with less exotic sources than wormholes whose throats have a spherical topology. Examples of exact wormhole solutions are given with scalar, spinor and electromagnetic fields as sources, and these fields are not necessarily phantom. In particular, there are wormhole solutions for a massless, minimally coupled scalar field in the presence of a negative cosmological constant, and for an azimuthal Maxwell electromagnetic field. All these solutions are not asymptotically flat. A no-go theorem is proved, according to which a flat (or string) asymptotic behavior on both sides of a cylindrical wormhole throat is impossible if the energy density of matter is everywhere nonnegative.
Within the scope of a static cylindrically symmetric space-time we study the behavior of a nonlinear spinor field that depends on time and radial coordinates. It is found that the presence of nontrivial non-diagonal components of the energy-momentum tensor (EMT) imposes some restriction on both the metric functions and the spinor field. While for the time independent spinor field there occur three way restrictions resembling the Bianchi type-I Universe, in this case things become more complicated.
The $f(R)$ theory is considered for static cylindrically symmetric and plane-symmetric spacetimes. In order to find solutions to the field equations of these models, the Noether symmetry method is used. First, we examine the GR case for cylindrically symmetrical space-time with the $w=-1$ dark energy state. Then, with the assumption of $f(R) = f_0R^n$, cases with matter and non-matter are examined and general solutions are determined for both space-times. Thus, it is shown that inclusive new solutions are obtained, considering the Noether symmetric conditions. In addition, the GR limit for eac…
Starting from the stationary cylindrically symmetric solution, but with the coordinates $z$ and $ϕ$ interchanged, and supposing that it could describe the vacuum spacetime of a translating cylinder, we investigate its physical and geometrical properties. This hypothesis is not entirely new since it has already been considered in a previous paper describing a translating source. We show that this metric is geometrically related to the vacuum field produced by a stationary rotating cylindrical source{, known as Lewis solution. However, we find new physical properties, different from those of the…
We investigate a class of cylindrically symmetric inhomogeneous $Λ$-dust spacetimes which have a regular axis and some zero expansion component. For $Λ\ne 0$, we obtain new exact solutions to the Einstein equations and show that they are unique, within that class. For $Λ=0$, we recover the Senovilla-Vera metric and show that it can be locally matched to an Einstein-Rosen type of exterior. Finally, we explore some consequences of the matching, such as trapped surface formation and gravitational radiation in the exterior.
In this paper we derive some new invariant solutions of Einstein-Maxwell's field equations for string fluid as source of matter in cylindrically symmetric space-time with Variable Magnetic Permeability. We also discuss the physical and eometrical properties of the models derived in the paper. The solutions, at least one of them, are interesting physically as they can explain the accelerating as well as singularity free Universe.
We studied the behavior of nonlinear spinor field within the scope of a static cylindrically symmetric space-time. It is found that the energy-momentum tensor (EMT) of the spinor field in this case possesses nontrivial non-diagonal components. The presence of non-diagonal components of the EMT imposes three-way restrictions wither on the space-time geometry or on the components of the spinor field or on both. It should be noted that analogical situation occurs in cosmology when nonlinear spinor field is exploited as a source of gravitational field given by Bianchi type-I cosmological model.
We consider the motion of test particles and light rays in a static cylindrically symmetric conformal spacetime given by Said et al [1]. We derive the equations of motion and present their analytical solutions in terms of the Weierstrass {\wp} function and the Kleinian σ function. Using parametric diagrams and effective potentials we analyze the possible orbits and characterize them in terms of the energy and the angular momentum of the test particles. Finally we show some examples of orbits.
We survey results about exact cylindrically symmetric models of gravitational collapse in General Relativity. We focus on models which result from the matching of two spacetimes having collapsing interiors which develop trapped surfaces and vaccum exteriors containing gravitational waves. We collect some theorems from the literature which help to decide a priori about eventual spacetime matchings. We revise, in more detail, some toy models which include some of the main mathematical and physical issues that arise in this context, and compute the gravitational energy flux through the matching b…
In this paper we consider a static, cylindrically symmetric spacetime with coincident f(Q) gravity. Since the field equation of this spacetime in symmetric teleparallel gravity is suitable for choosing the function of f(Q) in the form of power series and exponential forms, perfect fluid solutions of these forms are discussed. Energy densities, directional pressures and energy conditions are plotted and analysed for a few different metric potentials. Although cosmic strings violate all energy conditions in both f(Q) functions, the Levi-Civita solution violates all energy conditions in the power…
The present work deals with the dynamics of radiating star which is considered to be expansion free cylindrical symmetric dust dissipative fluids. Several treatments are adopted for the description of geometrical and physical features of such stars. Firstly, it is shown that, the dynamical star does not permit the streaming out limit and diffusion approximation and also proved that acceleration and dissipation are necessary for its dynamical evolution. It has also shown that, a static expansion free cylinder must be non-radiating. Secondly, the existence of cavity model and self-similar soluti…
This paper is devoted to analyze the dynamical instability of a self-gravitating object undergoes to collapse process. We take the framework of generalized teleparallel gravity with cylindrically symmetric gravitating object. The matter distribution is represented by locally anisotropic energy-momentum tensor. We develop basic equations such as dynamical equations along with matching conditions and Harrison-Wheeler equation of state. By applying linear perturbation strategy, we construct collapse equation which is used to accomplish the instability ranges in Newtonian and post-Newtonian regime…
The main purpose of this paper is to investigate the exact solutions of cylindrically symmetric spacetime in the context of $f(R,T)$ gravity [1], where $f(R,T)$ is an arbitrary function of Ricci scalar $R$ and trace of the energy momentum tensor $T$. We explore the exact solutions for two different classes of $f(R,T)$ models. The first class $f(R,T)=R+2f(T)$ yields a solution which corresponds to an exterior metric of cosmic string while the second class $f(R,T)=f_1(R)+f_2(T)$ provides an additional solution representing a non-null electromagnetic field. The energy densities and corresponding …
