Charged cylindrical collapse of anisotropic fluid

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.     

Instability analysis of a cylindrical stellar object in Brans–Dicke gravity

This paper investigates instability ranges of a cylindrically symmetric collapsing cosmic filamentary structure in the Brans–Dicke theory of gravity. For this purpose, we use a perturbating approach to the modified field equations as well as dynamic equations and construct a collapse equation. The collapse equation with an adiabatic index (Γ) is used to explore the instability ranges of both isotropic and anisotropic fluid in Newtonian and post-Newtonian approximations. It turns out that the instability ranges depend on the dynamic variables of collapsing filaments. We conclude that the system always remains unstable for 0 < Γ < 1, while Γ > 1 provides instability only in a special case.     

Collapse of a null fluid

An exact cylindrically symmetric solution of Einstein's gravitational field equations is given for a null fluid imploding radially along an infinite axis. This solution plays an important rôle in the late stages of collapse of a long cylinder of matter. One might expect that self-gravitational effects due to the increasingly relativistic mass of the collapsing matter would create arbitrarily large gravitational fields. It is shown, however, that in the null-fluid approximation the metric is everywhere regular.     

Cylindrically symmetric distributions of matter taking into account pressure

A cylindrically symmetric distribution of matter under pressure which evolves with time is considered. A new class of non-steady-state solutions to the Einstein equations with cylindrical symmetry is found (for cases when the matter is under zero, constant, and time-dependent pressure). A homogeneous, anisotropic universe and an analog of the Schwarzschild solution are considered as particular cases.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 33–36, December, 1985.     

Thin cylindrical shells in general relativity

The sources of static cylindrically symmetric fields in the form of thin cylindrical shells are studied. The results are compared (in the case of the thin shell consisting of orbiting particles with the result of Raychaudhuri and Som). A special solution is also found, represented by a collapsing shell which is the source of the static field.     

Domain Walls Strange Quark Matter in Einstein-Rosen Space-Time with Cosmological Constant and Heat Flow

In this paper, we have studied the solutions of Einstein field equations for domain walls with cosmological constant and heat flow in Einstein-Rosen cylindrical symmetric space-time when strange quark matter and normal matter attached to the domain walls. Some physical and kinematical features of the obtained cosmological model are studied and discussed.     

Structure scalars for charged cylindrically symmetric relativistic fluids

We investigate some structure scalars developed through Riemann tensor for self-gravitating cylindrically symmetric charged dissipative anisotropic fluid. We show that these scalars are directly related to the fundamental properties of the fluid. We formulate dynamical-transport equation as well as the mass function by including charge which are then expressed in terms of structure scalars. The effects of electric charge are investigated in the structure and evolution of compact objects. Finally, we show that all possible solutions of the field equations can be written in terms of these scalars.     

Fermi field and Dirac oscillator in a Som–Raychaudhuri space-time

We investigate the relativistic dynamics of a Dirac field in the Som–Raychaudhuri space-time, which is described by a Gödel-type metric and a stationary cylindrical symmetric solution of Einstein field equations for a charged dust distribution in rigid rotation. In order to analyze the effect of various physical parameters of this space-time, we solve the Dirac equation in the Som–Raychaudhuri space-time and obtain the energy levels and eigenfunctions of the Dirac operator by using the Nikiforov–Uvarov method. We also examine the behaviour of the Dirac oscillator in the Som–Raychaudhuri space-time, in particular, the effect of its frequency and the vorticity parameter.     

Instability ranges of collapsing star through adiabatic index in f(T, Θ) theory of gravity

The main purpose of this paper is to study the stability analysis of collapsing star in the scenario of Newtonian and post Newtonian approximations. We consider the cylindrical symmetry of collapsing object which is filled with anisotropic fluid. The f(T, Θ) theory of gravity, where T is the torsion scalar and Θ is the trace of energy-momentum tensor is taken into account. The dynamical field equations are constructed which help to derive collapse equation by applying the perturbation method. The stability behavior of collapsing star is defined in both Newtonian and post Newtonian approximations with the help of an adiabatic index.     

Effects of charge on dynamical instability of spherical collapse in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) gravity

The effects of charge on stable structure of spherically symmetric collapsing model comprising anisotropic matter distribution are studied in f(R, T) gravity, where R and T correspond to scalar curvature and trace of the energy-momentum tensor, respectively. We construct the field equations, Maxwell equations and dynamical equations in this scenario. We employ linear perturbation scheme on physical variables, metric functions as well as modified terms to establish the evolution or collapse equation for a consistent functional form of f(R, T) gravity. We investigate the limit of instability in Newtonian as well as post Newtonian regimes. It is found that charge plays a fundamental role to slow down the collapse and form a more stable system.     

Structural elements and collapse regimes in 3D flows on a slope

The mechanisms and structural elements of an instability whose development results in the collapse of flow fragments have been studied in the scope of the Hamilton version of the “shallow water” 3D model on a slope. The study indicated that the 3D model differs from its 2D analog in a more varied set of collapsing solutions. In particular, the solutions describing anisotropic collapse, during which the area of a collapsing fragment in contact with the slope contracts into a segment rather than a point, exist together with the solutions describing radially symmetric (isotropic) collapse.     

Spherically symmetric inhomogeneous dust collapse in higher dimensional space-time and cosmic censorship hypothesis

We consider a collapsing spherically symmetric inhomogeneous dust cloud in higher dimensional space-time. We show that the central singularity of collapse can be a strong curvature or a weak curvature naked singularity depending on the initial density distribution.     

Anisotropic spheres with Van der Waals-type equation of state

We study static spherically symmetric space-time to describe relativistic compact objects with anisotropic matter distribution and derive two classes of exact models to the Einstein–Maxwell system with a modified Van der Waals equation of state. We motivate a Van der Waals-type equation of state to physically signify a high-density domain of quark matter, and the generated exact solutions are shown to contain several classes of exact models reported previously that correspond to various physical scenarios. Geometrical analysis shows that the physical quantities are well behaved so that these models may be used to describe anisotropic charged compact spheres.     

Space–time inhomogeneity, anisotropy and gravitational collapse

We investigate the evolution of non-adiabatic collapse of a shear-free spherically symmetric stellar configuration with anisotropic stresses accompanied with radial heat flux. The collapse begins from a curvature singularity with infinite mass and size on an inhomogeneous space–time background. The collapse is found to proceed without formation of an even horizon to singularity when the collapsing configuration radiates all its mass energy. The impact of inhomogeneity on various parameters of the collapsing stellar configuration is examined in some specific space–time backgrounds.     

Gravitational collapse of dissipative fluid as a source of gravitational waves

Gravitational collapse of cylindrical anisotropic fluid has been considered in analogy with the work of Misner and Sharp. Using Darmois matching conditions, the interior cylindrical dissipative fluid (in the form of shear viscosity and heat flux) is matched to an exterior vacuum Einstein–Rosen space–time. It is found that on the bounding 3-surface the radial pressure of the anisotropic perfect fluid is linearly related to the shear viscosity and the heat flux of the dissipative fluid on the boundary. This non-zero radial pressure on the bounding surface may be considered as the source of gravitational waves outside the collapsing matter distribution.     

Anisotropic compact stars in Karmarkar spacetime

We present a new class of solutions to the Einstein field equations for an anisotropic matter distribution in which the interior space-time obeys the Karmarkar condition. The necessary and sufficient condition required for a spherically symmetric space-time to be of Class One reduces the gravitational behavior of the model to a single metric function. By assuming a physically viable form for the grr metric potential we obtain an exact solution of the Einstein field equations which is free from any singularities and satisfies all the physical criteria. We use this solution to predict the masses and radii of well-known compact objects such as Cen X-3, PSR J0348+0432, PSR B0943+10and XTE J1739-285.     

Dynamics of charged anisotropic spherical collapse in energy-momentum squared gravity

This paper investigates the dynamics of charged spherical collapse with anisotropic matter configuration in the context of energy-momentum squared gravity. This newly developed proposal resolves the big-bang singularity and yields the physically viable cosmological results in the early time universe. We establish dynamical equations through Misner-Sharp technique and analyze the effects of charge, anisotropy, effective matter variables and dark source terms on the collapse rate. A relation between Weyl scalar, fluid parameters and dark source terms is also established. The spacetime is not conformally flat due to the presence of anisotropic pressure, multivariate functions and their derivatives. In order to obtain conformally flat spacetime, we consider a specific model of this gravity, neglect the impact of charge and assume the isotropic matter distribution which yields homogeneity of the energy density and conformally flat spacetime. We conclude that positive dark source terms, anisotropy and charge yield the action of a repulsive force which enhances the stability of the system and hence diminishes the collapse rate.     

Analysis of a charged unidirectional perfect fluid gravitational collapse in cylindrical spacetime

The gravitational collapse of charged imperfect fluids (including the presence of strings) models the structural evolution of the Universe. The dynamics of a charged cylindrically symmetric spacetime investigates the effects of charge on the rate of gravitational collapse. In this respect, the Einstein–Maxwell equations are formed and solved to obtain the values of the dynamical parameters of the fluid including density, pressure and electric field. These parameters are graphically presented. It was concluded that the string tension effects all the physical parameters of the fluid. Moreover, the density and electric field intensity increases while the fluid’s pressure decreases near the time of singularity formation.     

A class of exact strange quark star model

Static spherically symmetric space-time is studied to describe dense compact star with quark matter within the framework of MIT Bag Model. The system of Einstein’s field equations for anisotropic matter is expressed as a new system of differential equations using transformations and it is solved for a particular general form of gravitational potential with parameters. For a particular parameter, as an example, it is shown that the model satisfies all major physical features expected in a realistic star. The generated model also smoothly matches with the Schwarzschild exterior metric at the boundary of the star. It is shown that the generated solutions are useful to model strange quark stars.     

Cylindrical wave solutions of a scalar-tensor theory

A class of exact solutions of the cylindrically symmetric space-time with two degrees of freedom corresponding to the vacuum field equations of a scalar-tensor theory proposed by Dunn is obtained. The solutions possess wavelike character.