This paper is devoted to study the charged perfect fluid cylindrical gravitational collapse. For this purpose, we find a new analytical solution of the field equations for non-static cylindrically symmetric spacetime. We discuss physical properties of the solution which predict gravitational collapse. It is concluded that in the presence of electromagnetic field the outgoing gravitational waves are absent. Further, it turns out that when longitudinal length reduces to zero due to resultant action of gravity and electromagnetic field, then the end state of the gravitational collapse is a conical singularity. We also explore the smooth matching of the collapsing cylindrical solution to a static cylindrically symmetric solution. In this matching, we take a special choice of constant radius of the boundary surface. We conclude that the gravitational and Coulomb forces of the system balance each other.
Solutions describing the gravitational collapse of asymptotically flat cylindrical and prolate shells of (null) dust are shown to admit globally naked singularities.
The present works deals with gravitational collapse of cylindrical viscous heat conducting anisotropic fluid following the work of Misner and Sharp. Using Darmois matching conditions, the dynamical equations are derived and the effect of charge and dissipative quantities over the cylindrical collapse are analyzed. Finally, using the Miller-Israel-Steward causal thermodynamic theory, the transport equation for heat flux are derived and its influence on collapsing system has been studied.
Following the scheme developed by Misner and Sharp, we discuss the dynamics of gravitational collapse. For this purpose, an interior cylindrically symmetric spacetime is matched to an exterior charged static cylindrically symmetric spacetime using the Darmois matching conditions. Dynamical equations are obtained with matter dissipating in the form of shear viscosity. The effect of charge and dissipative quantities over the cylindrical collapse are studied. Finally, we show that homogeneity in energy density and conformal flatness of spacetime are necessary and sufficient for each other.
We have studied the dynamics of a cylindrical column of anisotropic, charged fluid which is experiencing dissipation in the form of heat flow, free-streaming radiation, and shearing viscosity, undergoing gravitational collapse. We calculate the Einstein-Maxwell field equations and, using the Darmois junction conditions, match the interior non-static cylindrically symmetric space-time with the exterior anisotropic, charged, cylindrically symmetric space-time. The behavior of the density, pressure and luminosity of the collapsing matter has been analyzed. From the dynamical equations, the effect…
The present work deals with dynamics of gravitational collapse with cylindrical symmetry as developed by Misner and Sharp. The interior collapsing anisotropic cylindrical perfect fluid is matched to an exterior vacuum cylindrically symmetric space-time due to Einstein--Rosen using the Darmois matching conditions. It is found that the radial pressure of the anisotropic perfect fluid is non-zero on the boundary surface and is related to the components of shear viscosity. As a result, there is formation of gravitational waves outside the collapsing matter.
We study the gravitational collapse of a rotating cylindrical null shell with flat interior and the metric of a spinning cosmic string as the exterior. We see that there is a critical radius, where the energy density of the shell vanishes and beyond which it would be negative, thereby signaling that the matching would be unphysical.
We find analytical solutions describing the collapse of an infinitely long cylindrical shell of counter-rotating dust. We show that--for the classes of solutions discussed herein--from regular initial data a curvature singularity inevitably develops, and no apparent horizons form, thus in accord with the spirit of the hoop conjecture.
This paper is devoted to study the dynamics of gravitational collapse in the Misner and Sharp formalism. We take non-viscous heat conducting charged anisotropic fluid as a collapsing matter with cylindrical symmetry. The dynamical equations are derived and coupled with the transport equation for heat flux obtained from the M$\ddot{u}$ller-Israel-Stewart causal thermodynamic theory. We discuss the role of anisotropy, electric charge and radial heat flux over the dynamics of the collapse with the help of coupled equation.
The gravitational collapse of cylindrically distributed perfect fluid is studied. We assume the collapsing speed of fluid is very large and investigate such a situation by recently proposed high-speed approximation scheme. We show that if the value of the pressure divided by the energy density is bounded below by some positive value, the high-speed collapse is necessarily halted. This suggests that the collapsing perfect fluid of realistic ideal gas experiences the pressure bounce. However even in the case of mono-atomic ideal gas, arbitrarily large tidal force for freely falling observers are…
Perfect-fluid, static, cylindrically symmetric solutions of Einstein's field equations are obtained for the equations of state $ρ+3p=0$ and $ρ=p$. In the former case, the density and the pressure turn out to be constant while in the later case, they depend on the radial parameter $r$. Evan's solution corresponding to the equation of state $ρ=p$ is included in the solutions discussed here.
The objective of this paper is to discuss the dynamical instability in the context of Newtonian and post Newtonian regimes. For this purpose, we consider non-viscous heat conducting charged isotropic fluid as a collapsing matter with cylindrical symmetry. Darmois junction conditions are formulated. The perturbation scheme is applied to investigate the influence of dissipation and electromagnetic field on the dynamical instability. We conclude that the adiabatic index $Γ$ has smaller value for such a fluid in cylindrically symmetric than isotropic sphere.
The aim of this paper is to examine some obtained exact solutions of the Einstein-Maxwell equations, especially their properties from a chronological point of view. Each our spacetime is stationary cylindrically symmetric and it is filled up with an perfect fluid that is electrically charged. There are two classes of solutions and examples of each of them are investigated. We give examples of the first class both for the vanishing as well as for the non-vanishing Lorentz force.
Using the Sparling form and a geometric construction adapted to spacetimes with a 2-dimensional isometry group, we analyse a quasi-local measure of gravitational energy. We then study the gravitational radiation through spacetime junctions in cylindrically symmetric models of gravitational collapse to singularities. The models result from the matching of collapsing dust fluids interiors with gravitational wave exteriors, given by the Einstein-Rosen type solutions. For a given choice of a frame adapted to the symmetry of the matching hypersurface, we are able to compute the total gravitational …
Four-dimensional cylindrically symmetric spacetimes with homothetic self-similarity are studied in the context of Einstein's Theory of Gravity, and a class of exact solutions to the Einstein-massless scalar field equations is found. Their local and global properties are investigated and found that they represent gravitational collapse of a massless scalar field. In some cases the collapse forms black holes with cylindrical symmetry, while in the other cases it does not. The linear perturbations of these solutions are also studied and given in closed form. From the spectra of the unstable eigen…
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.
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…
This paper is devoted to find out cylindrically symmetric kinematic self-similar perfect fluid and dust solutions. We study the cylindrically symmetric solutions which admit kinematic self-similar vectors of second, zeroth and infinite kinds, not only for the tilted fluid case but also for the parallel and orthogonal cases. It is found that the parallel case gives contradiction both in perfect fluid and dust cases. The orthogonal perfect fluid case yields a vacuum solution while the orthogonal dust case gives contradiction. It is worth mentioning that the tilted case provides solution both for…
The gravitational collapse of an infinite cylindrical thin shell of generic matter in an otherwise empty spacetime is considered. We show that geometries admitting two hypersurface orthogonal Killing vectors cannot contain trapped surfaces in the vacuum portion of spacetime causally available to geodesic timelike observers. At asymptotic future null infinity, however, congruences of outgoing radial null geodesics become marginally trapped, due to convergence induced by shear caused by the interaction of a transverse wave component with the geodesics. The matter shell itself is shown to be alwa…
We construct approximate solutions that will describe the last stage of cylindrically symmetric gravitational collapse of dust fluid. Just before the spacetime singularity formation, the speed of the dust fluid might be almost equal to the speed of light by gravitational acceleration. Therefore the analytic solution describing the dynamics of cylindrical null dust might be the crudest approximate solution of the last stage of the gravitational collapse. In this paper, we regard this null dust solution as a background and perform `high-speed approximation' to know the gravitational collapse of …
The general formulas of a non-rotating dynamic thin shell that connects two arbitrary cylindrical regions are given using Israel's method. As an application of them, the dynamics of a thin shell made of counter-rotating dust particles, which emits both gravitational waves and massless particles when it is expanding or collapsing, is studied. It is found that when the models represent a collapsing shell, in some cases the angular momentum of the dust particles is strong enough to halt the collapse, so that a spacetime singularity is prevented from forming, while in other cases it is not, and a …
The aim of this paper is to investigate the dynamical aspects of charged viscous cylindrical source by using Misner approach. To this end, we have considered the more general charged dissipative fluid enclosed by the cylindrical symmetric spacetime. The dissipative nature of the source is due to the presence of dissipative variables in the stress-energy tensor. The dynamical equations resulting from such charged cylindrical dissipative source have been coupled with the causal transport equations for heat flux, shear and bulk viscosity, in the context of Israel-Steward theory. In this case, we …
In this paper, we study the gravitational collapse of null dust in the cylindrically symmetric spacetime. The naked singularity necessarily forms at the symmetry axis. We consider the situation in which null dust is emitted again from the naked singularity formed by the collapsed null dust and investigate the back-reaction by this emission for the naked singularity. We show a very peculiar but physically important case in which the same amount of null dust as that of the collapsed one is emitted from the naked singularity as soon as the ingoing null dust hits the symmetry axis and forms the na…
A cylindrically symmetric perfect fluid spacetime with no curvature singularity is shown. The equation of state for the perfect fluid is that of a stiff fluid. The metric is diagonal and non-separable in comoving coordinates for the fluid. It is proven that the spacetime is geodesically complete and globally hyperbolic.
This paper is devoted to investigate the cylindrical collapse of an anisotropic fluid in $f(R)$ gravity. For this purpose, the viscous charged anisotropic fluid dissipating energy with heat flow and shear is assumed. We use the perturbation scheme to develop the dynamical equations for the variables that ultimately lead to the disturbance of the physical variables and the Starobinksy like $f(R)$ model chosen. The evolution of the matter variables is discussed with the help of these equations. It can be concluded that the range of dynamic instabilities depends on the field strength, density dis…
In this paper, the study of the gravitational collapse of cylindrically distributed two perfect fluid system has been carried out. It is assumed that the collapsing speeds of the two fluids are very large. We explore this condition by using the high-speed approximation scheme. There arise two cases, i.e., bounded and vanishing of the ratios of the pressures with densities of two fluids given by $c_s, d_s$. It is shown that the high-speed approximation scheme breaks down by non-zero pressures $p_1, p_2$ when $c_s, d_s$ are bounded below by some positive constants. The failure of the high-speed …
By the end of the evaluation of this research artifact, readers would be able to describe the effect of conducted plasma on evolution of stellar objects. In this script, we have analyzed the stability of charged cylindrically symmetric stellar objects in the context of f(R; T) theory of gravity. We have fabricated field equations and their conforming dynamical equations and then we have used perturbation scheme for additional analysis. Adiabatic index Γ has been used to sort inequalities in the Newtonian and the post Newtonian regimes. At the end we caught some extra limitations due to which w…
Dust configurations are the simplest models for astrophysical objects. Here we examine the gravitational collapse of an infinite cylinder of dust and give an analytic interior solution. Surprisingly, starting with a cylindrically symmetric ansatz one arrives at a 3-space with constant curvature, i.e. the resulting metric describes a piece of the Friedman interior of the Oppenheimer-Snyder collapse. Indeed, by introducing double polar coordinates, a 3-space of constant curvature can be interpreted as a cylindrically symmetric space as well. This result shows afresh that topology is not fixed by…
We numerically study the dynamics of an imploding hollow cylinder composed of dust. Since there is no cylindrical black hole in 4-dimensional spacetime with physically reasonable energy conditions, a collapsed dust cylinder involves a naked singularity accompanied by its causal future, or a fatal singularity which terminates the history of the whole universe. In a previous paper, the present authors have shown that if the dust is assumed to be composed of collisionless particles such that these particles go through the symmetry axis of the cylinder, then the scalar polynomial singularity forme…
The gravitational collapse of a thick cylindrical shell of dust matter is investigated. It is found that a spacetime singularity forms on the symmetry axis and that it is necessarily naked, i.e., observable in principle. We propose a physically reasonable boundary condition at this naked singularity to construct the solution including its causal future. This boundary condition enables us to construct the unique continuation of spacetime beyond the naked singularity and ensures that the dust shell passes through the naked singularity. When the cylindrical shell leaves its symmetry axis away, th…
We construct an approximate solution which describes the gravitational emission from a naked singularity formed by the gravitational collapse of a cylindrical thick shell composed of dust. The assumed situation is that the collapsing speed of the dust is very large. In this situation, the metric variables are obtained approximately by a kind of linear perturbation analysis in the background Morgan solution which describes the motion of cylindrical null dust. The most important problem in this study is what boundary conditions for metric and matter variables should be imposed at the naked singu…
Very recently, a ``Comment'' by Wang [gr-qc/0309003] on a paper by Gonçalves [Phys. Rev. D {\bf 65}, 084045 (2002)] appeared, claiming that Gonçalves' analysis of trapped surfaces in certain kinds of cylindrical spacetimes was incomplete. Specifically, Wang claims to have found a coordinate extension of the spacetime used by Gonçalves (the Einstein-Rosen spacetime) which contains trapped surfaces; in addition, Wang also claims that some such trapped surfaces are apparent horizons. Here, I comment on Wang's ``Comment'', and argue that, while Wang's spacetime extension appears to exist and conta…
The dynamics of collapsing and expanding cylindrically symmetric gravitational and matter fields with lightlike wave-fronts is studied in General Relativity, using the Barrabes-Israel method. As an application of the general formulae developed, the collapse of a matter field that satisfies the condition R_{AB}g^{AB} = 0, (A, B = z, phi), in an otherwise flat spacetime background is studied. In particular, it is found that the gravitational collapse of a purely gravitational wave or a null dust fluid cannot be realized in a flat spacetime background. The studies are further specified to the col…
In this paper, we evaluate kinematic self-similar perfect fluid and dust solutions for the most general cylindrically symmetric spacetime. We explore kinematic self-similar solutions of the first, second, zeroth and infinite kinds for parallel and orthogonal cases. It is found that the parallel case gives solutions for both perfect fluid and dust cases in all kinds except the zeroth kind of the dust case where there exists no solution. The orthogonal perfect fluid case gives stiff fluid solution only in the first kind and vacuum solution for the dust case. We obtain a total of thirteen solutio…
We study the matching conditions for a collapsing anisotropic cylindrical perfect fluid, and we show that its radial pressure is non zero on the surface of the cylinder and proportional to the time dependent part of the field produced by the collapsing fluid. This result resembles the one that arises for the radiation - though non-gravitational - in the spherically symmetric collapsing dissipative fluid, in the diffusion approximation.
We investigate self-similar scalar field solutions to the Einstein equations in whole cylinder symmetry. Imposing self-similarity on the spacetime gives rise to a set of single variable functions describing the metric. Furthermore, it is shown that the scalar field is dependent on a single unknown function of the same variable and that the scalar field potential has exponential form. The Einstein equations then take the form of a set of ODEs. Self-similarity also gives rise to a singularity at the scaling origin. We discuss the number of degrees of freedom at an arbitrary point and prove exist…
We consider diagonal cylindrically symmetric metrics, with an interior representing a general non-rotating fluid with anisotropic pressures. An exterior vacuum Einstein-Rosen spacetime is matched to this using Darmois matching conditions. We show that the matching conditions can be explicitly solved for the boundary values of metric components and their derivatives, either for the interior or exterior. Specializing to shearfree interiors, a static exterior can only be matched to a static interior, and the evolution in the non-static case is found to be given in general by an elliptic function …
We investigate self-similar scalar field solutions to the Einstein equations in whole cylinder symmetry. Imposing self-similarity on the spacetime gives rise to a set of single variable functions describing the metric. Furthermore, it is shown that the scalar field is dependent on a single unknown function of the same variable and that the scalar field potential has exponential form. The Einstein equations then take the form of a set of ODEs. Self-similarity also gives rise to a singularity at the scaling origin. We extend the work of [1], which determined the global structure of all solutions…
We present a cylindrically symmetric, Petrov type D, nonexpanding, shear free and vorticity free solution of Einstein's field equations. The spacetime is asymptotically flat radially and regular everywhere except on the symmetry axis where it possesses a naked curvature singularity. The energy momentum tensor of the spacetime is that for an anisotropic fluid which satisfies the different energy conditions. This spacetime is used to generate a rotating spacetime which admits closed timelike curves and may represent a Cosmic Time Machine.
This paper investigates instability ranges of a cylindrically symmetric collapsing stellar object in Brans-Dicke theory of gravity. For this purpose, we use perturbation approach in the modified field equations as well as dynamical equations and construct a collapse equation. The collapse equation with adiabatic index ($Γ$) is used to explore the instability ranges of both isotropic as well as anisotropic fluid in Newtonian and post-Newtonian approximations. It turns out that the instability ranges depend on the dynamical variables of collapsing fluid. We conclude that the system always remain…
The present work investigates the gravitational collapse of a perfect fluid in $f(R)$ gravity models. For a general $f(R)$ theory, it is shown analytically that a collapse is quite possible. The singularity formed as a result of the collapse is found to be a curvature singularity of shell focusing type. The possibility of the formation of an apparent horizon hiding the central singularity depends on the initial conditions.
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…
Gravitational collapse of non-spherical symmetric matter leads inevitably to non-static external spacetimes. It is shown here that gravitational collapse of matter with toroidal topology in a toroidal anti-de Sitter background proceeds to form a toroidal black hole. According to the analytical model presented, the collapsing matter absorbs energy in the form of radiation (be it scalar, neutrinos, electromagnetic, or gravitational) from the exterior spacetime. Upon decompactification of one or two coordinates of the torus one gets collapsing solutions of cylindrical or planar matter onto black …
The spherical gravitational collapse of a compact packet consisting of perfect fluid is studied. The spacetime outside the fluid packet is described by the out-going Vaidya radiation fluid. It is found that when the collapse has continuous self-similarity the formation of black holes always starts with zero mass, and when the collapse has no self-similarity, the formation of black holes always starts with a finite non-zero mass. The packet is usually accompanied by a thin matter shell. The effects of the shell on the collapse are also studied.
We consider static cylindrically symmetric charged gravitating object with perfect fluid and investigate the gravitational binding energy. It is found that only the localized part of the mass function provides the gravitational binding energy, whereas the non-localized part generated by the electric coupling does not contribute for such energy.
Perfect fluid with kinematic self-similarity is studied in 2+1 dimensional spacetimes with circular symmetry, and various exact solutions to the Einstein field equations are given. In particular, these include all the solutions of dust and stiff perfect fluid with self-similarity of the first kind, and all the solutions of perfect fluid with a linear equation of state and self-similarity of the zeroth or second kind. It is found that some of these solutions represent gravitational collapse, and the final state of the collapse can be either black holes or naked singularities.
We perform quantization of a model in which gravity is coupled to a circular dust shell in 2+1 spacetime dimensions. Canonical analysis shows that momentum space of this model is ADS^2-space, and the global chart for it is provided by the Euler angles. In quantum kinematics, this results in non-commutativity in coordinate space and discreteness of the shell radius in timelike region, which includes the collapse point. At the level of quantum dynamics, we find transition amplitudes between zero and non-zero eigenvalues of the shell radius, which describe the rate of gravitational collapse (boun…
We investigate the occurrence and nature of naked singularities in the gravitational collapse of an adiabatic perfect fluid in self-similar higher dimensional space-times. It is shown that strong curvature naked singularities could occur if the weak energy condition holds. Its implication for cosmic censorship conjecture is discussed. Known results of analogous studies in four dimensions can be recovered.
We prove existence of static solutions to the cylindrically symmetric Einstein-Vlasov system, and we show that the matter cylinder has finite extension. The same results are also proved for a quite general class of equations of state for perfect fluids coupled to the Einstein equations, extending the class of equations of state considered in \cite{BL}. We also obtain this result for the Vlasov-Poisson system.
In this paper, the effect of a positive cosmological constant on spherically symmetric collapse with perfect fluid has been investigated. The matching conditions between static exterior and non-static interior spacetimes are given in the presence of a cosmological constant. We also study the apparent horizons and their physical significance. It is concluded that the cosmological constant slows down the collapse of matter and hence limit the size of the black hole. This analysis gives the generalization of the dust case to the perfect fluid. We recover the results of the dust case for $p=0$.
Self-similar solutions of a collapsing perfect fluid and a massless scalar field with kinematic self-similarity of the first kind in 2+1 dimensions are obtained. Their local and global properties of the solutions are studied. It is found that some of them represent gravitational collapse, in which black holes are always formed, and some may be interpreted as representing cosmological models.
The hypothesis of cosmic censorship plays a crucial role in classical general relativity, namely, to ensure that naked singularities would never occur from the black hole singularity. In this paper, we will present how energy conditions prohibit forming the naked singularity in the spherical perfect fluid collapse, and thus the strong cosmic censorship conjecture hold in this model. We also show that this result can be extended to the cosmological constant background.
The stability analysis of self-similar solutions is an important approach to confirm whether they act as an attractor in general non-self-similar gravitational collapse. Assuming that the collapsing matter is a perfect fluid with the equation of state $P=αρ$, we study spherically symmetric non-self-similar perturbations in homogeneous self-similar collapse described by the flat Friedmann solution. In the low pressure approximation $α\ll 1$, we analytically derive an infinite set of the normal modes and their growth (or decay) rate. The existence of one unstable normal mode is found to conclude…
The Riemann, Ricci and Einstein tensors for N-dimensional spherically symmetric spacetimes in various systems of coordinates are studied, and the general metric for conformally flat spacetimes is given. As an application, all the Friedmann-Robertson-Walker-like solutions for a perfect fluid with an equation of state $p = k ρ$ are found. Then, these solutions are used to model the gravitational collapse of a compact ball, by first cutting them along a timelike hypersurface and then joining them with asymptotically flat Vaidya solutions. It is found that when the collapse has continuous self-sim…
This paper investigates the evolution of collapsing FRW models with a scalar field having the potential which arises in the conformal frame of high order gravity theories, coupled to matter described by a perfect fluid with energy density $ρ$ and pressure $p$, obeying a barotropic equation of state. The solutions are shown to evolve generically to a singular state in a finite time and they are used as sources for radiating objects undergoing complete gravitational collapse. Although these singularities may be naked in some special case, it is shown that generically a black hole forms.
We study the complete gravitational collapse of a class of spherically symmetric inhomogeneous perfect fluid models obtained by introducing small radial perturbations in an otherwise homogeneous matter cloud. Our aim here is to study the genericity and stability of the formation of black holes and locally naked singularities in collapse. While the occurrence of naked singularities is known for many models of collapse, the key issue now in focus is genericity and stability of these outcomes. Towards this purpose, we study how the introduction of a somewhat general class of small inhomogeneities…
