Dynamics of tilted and non-tilted Lemaitre-Tolman-Bondi spacetime in f(R) gravity

This paper investigates the dynamics of Lemaitre-Tolman-Bondi spacetime with respect to tilted observer in f(R) gravity and obtains significant relationships between tilted and non-tilted observers. We discuss inhomogeneity factor and its evolution with the help of kinematical and dynamical quantities. It is found that for tilted observer the evolution of inhomogeneity factor depends upon heat flux, shear tensor and expansion scalar while for non-tilted observer, it depends only upon shear tensor. We also explore the stability criteria of non-tilted congruence in the presence of dark source term and find that expansion is responsible for instability of non-tilted congruence.     

Electromagnetic field and dynamics of tilted Lemaitre-Tolman-Bondi spacetimes

In this paper, we investigate the dynamics of Lemaitre-Tolman-Bondi spacetimes with imperfect fluid in the presence of electromagnetic field. We study the effects of charge with respect to an observer moving radially relative to the fluid, that is, a tilted observer. The relationship between various quantities in the tilted and non-tilted congruences is developed using the Einstein-Maxwell field equations. We explore various factors affecting the inhomogeneities in the energy density of the fluid and also discuss the stability of the non-tilted congruence.     

Tilted and non-tilted Gödel-type universe

This paper explores the dynamics of Gödel-type geometry for tilted and non-tilted congruences. The kinematical as well as dynamical quantities are investigated for both congruences with non-vanishing nature of vorticity vector. The obtained vorticity is of kinematical type, i.e., not produced by a circular flow of superenergy on the plane orthogonal to the vorticity vector. We conclude that super-Poynting vector is non-zero for the tilted congruence linked with heat flux of fluid distribution while it vanishes in non-tilted case.     

On the stability of a class of radiating viscous self-gravitating stars with axial symmetry

This study investigates the stability of a class of radiating viscous self-gravitating stars with axial symmetry having anisotropic pressure. We use perturbation technique to establish the perturbed form of the Einstein field equations and dynamical equations. The instability range in the Newtonian and post-Newtonian eras has been analyzed by constructing the collapse equation. It is found that the adiabatic index has a key role in the discussion of instability ranges which depends upon the physical parameters, i.e., energy density, anisotropic pressure and shear viscosity of the fluid and heat flux. We conclude that the shear viscosity decreases the instability range and makes the system more stable.     

Singularity attenuation with quantum-mechanically revisited metric tensor

The space and initial singularities are reexamined in the most reliable solutions to the Einstein's field equations (EFE), that is, the Einstein–Gilbert–Straus (EGS) metric. In discretized Finsler geometry, additional curvatures and thereby geometric structures likely emerge, which are distinct from the conventional spacetime curvatures and geometric structures that the Einstein's theory of general relativity introduced. The generalized fundamental tensor, which is obtained in the Fisleriean geometry, imposes quantum-mechanically revisions on the Landau–Raychaudhuri evolution equations. The time-like geodesic congruence in EGS metric is then analyzed, analytically and numerically. The evolution of a family of trajectories whose congruence is defined by the flow lines generated by velocity fields is determined. We conclude that both two types of singularities seem to be attenuated or even regulate. With the singularity attenuation, we refer to the fundamental nature of the additional curvatures at quantum relativistic scales.     

Bianchi type-V cosmological model with purely magnetic solution

In the present paper we study some new aspects of the Bianchi type-V space time. The Electric and Magnetic parts of Weyl tensors are calculated in terms of tilted congruence and discussed the purely magnetic Weyl tensor. Einstein field equations for purely magnetic space time are obtained and solution of such field equations called purely magnetic solution. To get deterministic solutions of the field equations we consider a new law of variation of average scale factor which yields time dependent deceleration parameter. Certain physical and geometrical properties of the model are also discussed.     

Space-Time Geometry of Quark and Strange Quark Matter

We study quarkand strangequarkmatter in the contextof generalrelativity.For this purpose,we solve Einstein's field equations for quark and strange quark matter in spherical symmetric space-times. We analyze strange quark matter for the different equations of state (EOS) in the spherical symmetric space-times,thus we are able to obtain the space-time geometries of quark and strange quark matter. Also,we discuss the features of the obtained solutions. The obtained solutions are consistent with the results of Brookhaven Laboratory,i.e. the quark-gluon plasma has a vanishing shear (i.e. quark-gluon plasma is perfect).     

Crustal oscillations of slowly rotating relativistic stars

We study low-amplitude crustal oscillations of slowly rotating relativistic stars consisting of a central fluid core and an outer thin solid crust. We estimate the effect of rotation on the torsional toroidal modes and on the interfacial and shear spheroidal modes. The results compared against the Newtonian ones for wide range of neutron star models and equations of state.     

Anisotropic Tolman-like solutions of Einstein's equations

In this work we present new solutions of Einstein's equations assuming a spherically symmetric anisotropic fluid with shear in comoving coordinates. We study two limit cases: when the tangential pressure vanishes and when the radial pressure vanishes. The new solutions are based on the Tolman's solutions.     

Self-consistent gravitational lens reconstruction

We present a new method for directly determining accurate, self-consistent cluster lens mass and shear maps in the strong lensing regime from the magnification bias of background galaxies. The method relies upon pixellization of the surface mass density distribution which allows us to write down a simple, solvable set of equations. We also show how pixellization can be applied to methods of mass determination from measurements of shear and present a simplified method of application. The method is demonstrated with cluster models and applied to magnification data from the lensing cluster Abell 1689.     

Viscous fluid cosmology with a cosmological constant

Exact solutions of the field equations for a Bianchi type-I space-time, filled with a viscous fluid and cosmological constant, are obtained. We utilize the constancy of deceleration parameter to get singular and non-singular solutions. We investigate a number of solutions with constant and time-varying cosmological constant together with a linear relation between shear viscosity and expansion scalar. Due to dissipative processes, the mean anisotropy and shear of the model tend to zero at a faster rate.     

Some geometric properties of a dusty fluid in MFD flows

By reformulating the basic equations governing the steady, compressible dusty fluid in magneto-fluid flows, certain geometric results of physical importance are obtained. The congruence of the stream lines and magnetic field lines have been taken as the orthogonal coordinate curves on the Maxwellian surfaces.     

On radiating stellar collapse with shear

Relativistic models of radiating stellar collapse with shear require careful checking of all the equations and quantities involved. We illustrate this by showing that, in a recently proposed model, the metric ansatz is in fact too restrictive to allow any radial evolution to occur, and only tangential evolution is possible. Furthermore, the assumption of pressure isotropy is shown to reduce the model to the static case without radiation or shear.     

Plane symmetric inhomogeneous cosmological models with a perfect fluid in General Relativity II

We investigate a class of solutions of Einstein equations for the plane symmetric perfect fluid case. If these solutions have shear, they must necessarily be non-static. Some physical and geometric properties of the models are also discussed.      

Cosmic shear in inflationary models of Bianchi types VIII and IX

Two exact solutions of Einstein's field equations of vacuum are presented and investigated. We will regard the term vacuum fluid as the limiting case of scalar field with an almost constant potential. Considering the four velocity of this fluid we find, that in both solutions there is an anisotropic expansion of the cosmic fluid, but the fluid has vanishing vorticity.We investigate whether shear could prevent the transition into an inflationary era in these models, and the effect of shear on a scalar field is also considered. It is found that shear will speed up the rollover of the scalar field in some Bianchi type-VIII models.Possible initial conditions are discussed in light of the group structures of the models.     

Anisotropic Bianchi type-I models in string cosmology

The present study deals with a spatially homogeneous and anisotropic Bianchi-I cosmological models representing massive strings. The energy-momentum tensor, as formulated by Letelier (1983), has been used to construct massive string cosmological models for which we assume the expansion scalar in the models is proportional to one of the components of shear tensor. The Einstein’s field equations have been solved by applying a variation law for generalized Hubble’s parameter in Bianchi-I space-time. We have analysed a comparative study of accelerating and decelerating models in the presence of string scenario. The study reveals that massive strings dominate in the decelerating universe whereas strings dominate in the accelerating universe. The strings eventually disappear from the universe for sufficiently large times, which is in agreement with current astronomical observations.     

Dynamics of Bianchi I universe with magnetized anisotropic Dark Energy

We study Bianchi type I cosmological model in the presence of magnetized anisotropic dark energy. The energy-momentum tensor consists of anisotropic fluid with anisotropic EoS p=ω ρ and a uniform magnetic field of energy density ρ _B . We obtain exact solutions to the field equations using the condition that expansion is proportional to the shear scalar. The physical behavior of the model is discussed with and without magnetic field. We conclude that universe model as well as anisotropic fluid do not approach isotropy through the evolution of the universe.     

Energy density inhomogeneities with polynomial f(R) cosmology

In this paper, we study the effects of polynomial f(R) model on the stability of homogeneous energy density in self-gravitating spherical stellar object. For this purpose, we construct couple of evolution equations which relate the Weyl tensor with matter parameters. We explore different factors responsible for density inhomogeneities with non-dissipative dust, isotropic as well as anisotropic fluids and dissipative dust cloud. We find that shear, pressure, dissipative parameters and f(R) terms affect the existence of inhomogeneous energy density.     

Expanding Universe with bulk and shear viscosity in conformally flat coordinates

Conformally flat line-elements are applied to imperfect fluids in cosmology. Explicit solutions of the field equations are given for an equation of state for which the pressure is proportional to the density. Both the isotropic case (for which the shear viscosity vanishes) and the non-isotropic case are considered and expressions derived for the appropriate coefficients of shear and bulk viscosity, as well as density.     

The linear stability of dilute particulate rings

Irregular structure in planetary rings is often attributed to the intrinsic instabilities of a homogeneous state undergoing Keplerian shear. Previously these have been analysed with simple hydrodynamic models. We instead employ a kinetic theory, in which we solve the linearised moment equations derived in Shu and Stewart 1985 for a dilute ring. This facilitates an examination of velocity anisotropy and non-Newtonian stress, and their effects on the viscous and viscous/gravitational instabilities thought to occur in Saturn's rings. Because we adopt a dilute gas model, the applicability of our results to the actual dense rings of Saturn are significantly curtailled. Nevertheless this study is a necessary preliminary before an attack on the difficult problem of dense ring dynamics. We find the Shu and Stewart formalism admits analytic stability criteria for the viscous overstability, viscous instability, and thermal instability. These criteria are compared with those of a hydrodynamic model incorporating the effective viscosity and cooling function computed from the kinetic steady state. We find the two agree in the ‘hydrodynamic limit’ (i.e., many collisions per orbit) but disagree when collisions are less frequent, when we expect the viscous stress to be increasingly non-Newtonian and the velocity distribution increasingly anisotropic. In particular, hydrodynamics predicts viscous overstability for a larger portion of parameter space. We also numerically solve the linearised equations of the more accurate Goldreich and Tremaine 1978 kinetic model and discover its linear stability to be qualitatively the same as that of Shu and Stewart's. Thus the simple collision operator adopted in the latter would appear to be an adequate approximation for dilute rings, at least in the linear regime.