scholarly journals Expansion-free cylindrically symmetric models

2012 ◽  
Vol 90 (9) ◽  
pp. 865-870 ◽  
Author(s):  
M. Sharif ◽  
Z. Yousaf
Keyword(s):  
Energy Density ◽  
Weyl Tensor ◽  
Thin Shell ◽  
Fluid Distribution ◽  
Anisotropic Fluid ◽  
Junction Condition ◽  
Free Condition ◽  
Cylindrically Symmetric ◽  
Vacuum Cavity ◽  
Boundary Surfaces

This paper investigates cylindrically symmetric distribution of an anisotropic fluid under the expansion-free condition, which requires the existence of a vacuum cavity within the fluid distribution. We have discussed two families of solutions that further provide two exact models in each family. Some of these solutions satisfy the Darmois junction condition while some show the presence of a thin shell on both boundary surfaces. We also formulate a relation between the Weyl tensor and energy density.

EVOLUTION OF EXPANSION-FREE SELF-GRAVITATING FLUIDS AND PLANE SYMMETRY

2012 ◽  
Vol 21 (14) ◽  
pp. 1250095 ◽  
Author(s):  
M. SHARIF ◽  
Z. YOUSAF
Keyword(s):  
Weyl Tensor ◽  
Thin Shell ◽  
Analytical Models ◽  
Symmetric Distribution ◽  
Anisotropic Fluid ◽  
Junction Conditions ◽  
Plane Symmetry ◽  
Free Condition ◽  
Plane Symmetric ◽  
Expansion Scalar

We investigate some analytical models of the plane symmetric distribution of anisotropic fluid with vanishing expansion scalar. Darmois junction conditions, on both the internal and external hypersurfaces, are given. A relationship between the Weyl tensor and the matter variables is developed. We explore four families of solutions under expansion-free condition some of which indicate the presence of thin shell, while some others satisfy junction conditions. It is shown that the Skripkin model is incompatible with junction conditions in the plane symmetry.

scholarly journals TRAPPING PHOTONS BY A LINE SINGULARITY

2003 ◽  
Vol 12 (06) ◽  
pp. 1095-1112 ◽  
Author(s):  
METIN ARIK ◽  
OZGUR DELICE
Keyword(s):  
Energy Density ◽  
Thin Shell ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Cylindrically Symmetric ◽  
Static Solutions ◽  
Line Singularity ◽  
Thick Shells

We present cylindrically symmetric, static solutions of the Einstein field equations around a line singularity such that the energy momentum tensor corresponds to infinitely thin photonic shells. Positivity of the energy density of the thin shell and the line singularity is discussed. It is also shown that thick shells containing mostly radiation are possible in a numerical solution.

Cylindrically symmetric relativistic fluids and the purely electric Weyl tensor

2015 ◽  
Vol 12 (10) ◽  
pp. 1550103 ◽  
Author(s):  
Rajesh Kumar ◽  
S. K. Srivastava ◽  
V. C. Srivastava
Keyword(s):  
General Relativity ◽  
Energy Density ◽  
Weyl Tensor ◽  
Einstein’S Equations ◽  
Relativistic Fluids ◽  
Einstein's Equations ◽  
Cylindrically Symmetric ◽  
Expansion Scalar

In General Relativity (GR), the analysis of electric and magnetic Weyl tensors has been studied by various authors. The present study deals with cylindrically symmetric relativistic fluids in GR characterized by the vanishing of magnetic Weyl tensor-purely electric (PE) fields. A very new assumption has been adapted to solve the Einstein's equations and the obtained solution is shearing at all. We signified the importance of PE fields in the context of expansion scalar, energy density, shear and acceleration.

Complexity factors for static anisotropic axially symmetric fluid distributions in f(R) gravity

2020 ◽  
Vol 17 (03) ◽  
pp. 2050043
Author(s):  
G. Abbas ◽  
H. Nazar
Keyword(s):  
Energy Density ◽  
General Theory ◽  
Graphical Analysis ◽  
Fluid Distribution ◽  
Anisotropic Fluid ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Axially Symmetric ◽  
Structure Scalars ◽  
Isotropic Pressure

In this paper, we have analyzed the complexity factor for the most general axially symmetric static anisotropic fluid distributions in context of [Formula: see text] theory of gravity. For this purpose, we have studied three distinct complexity factors that are organized in terms of three scalar variables (structure scalars) comes from the orthogonal splitting of the curvature tensor. The vanishing of all complexity factors condition for what we choose the simplest fluid distribution that in which system having energy density is homogeneous with isotropic pressure. Although, it has been found that the complexity factors condition can also vanish when inhomogeneous energy density and anisotropy of the pressure cancel each other. Next, we express a class of exact solutions and their graphical analysis as compatible to our models that satisfies the vanishing condition of complexity factors. Finally, it is worth mentioning that these results can reproduce the results of General theory of Relativity under some constraints.

scholarly journals Study of generalized cylindrical polytropes with complexity factor

2021 ◽  
Vol 81 (9) ◽  
Author(s):  
Shiraz Khan ◽  
S. A. Mardan ◽  
M. A. Rehman
Keyword(s):  
Equation Of State ◽  
Energy Density ◽  
Differential Equations ◽  
Mass Density ◽  
Modify Form ◽  
Graphical Analysis ◽  
Fluid Distribution ◽  
Anisotropic Fluid ◽  
Polytropic Equation ◽  
Frame Work

AbstractIn this paper, complexity factor is used with generalized polytropic equation of state to develop two consistent systems of three differential equations and a general frame work is established for modify form of Lane-Emden equations. For this purpose anisotropic fluid distribution is considered in cylindrical static symmetry with two cases of generalized polytropic equation of state (i) mass density $$\mu _{o}$$ μ o and (ii) energy density $$\mu $$ μ . A graphical analysis will be carried out for the numerical solution of these systems of three differential equations.

Evolution of expansion-free spherically symmetric self-gravitating non-dissipative fluids and some analytical solutions

2018 ◽  
Vol 15 (04) ◽  
pp. 1850058 ◽  
Author(s):  
Rajesh Kumar ◽  
Sudhir Kumar Srivastava
Keyword(s):  
Analytical Models ◽  
Fluid Distribution ◽  
Junction Condition ◽  
Spherically Symmetric ◽  
Junction Conditions ◽  
Minkowski Space Time ◽  
Spherically Symmetric Metric ◽  
Anisotropic Fluids ◽  
Vacuum Cavity ◽  
Dissipative Fluids

We consider the distribution of spherically symmetric self-gravitating non-dissipative (but anisotropic) fluids under the expansion-free condition which requires the existence of vacuum cavity within the fluid distribution. The Darmois junction condition is investigated for matching the spherically symmetric metric to an internal vacuum cavity (Minkowski space-time). We have studied some analytical models, total of three family of solutions out of which two satisfy the junction conditions over both the hypersurfaces. The models are investigated under some known dynamical assumptions which further provide analytical solution in each family.

scholarly journals EXPANSION-FREE CAVITY EVOLUTION: SOME EXACT ANALYTICAL MODELS

2011 ◽  
Vol 20 (12) ◽  
pp. 2351-2367 ◽  
Author(s):  
A. DI PRISCO ◽  
L. HERRERA ◽  
J. OSPINO ◽  
N. O. SANTOS ◽  
V. M. VIÑA-CERVANTES
Keyword(s):  
Analytical Models ◽  
Fluid Distribution ◽  
Expansion Scalar ◽  
Kinematical Condition ◽  
Cavity Evolution ◽  
Central Explosion ◽  
Anisotropic Fluids ◽  
Surrounding Fluid ◽  
Vacuum Cavity ◽  
Boundary Surfaces

We consider spherically symmetric distributions of anisotropic fluids with a central vacuum cavity, evolving under the condition of vanishing expansion scalar. Some analytical solutions are found satisfying Darmois junction conditions on both delimiting boundary surfaces, while some others require the presence of thin shells on either (or both) boundary surfaces. The solutions here obtained model the evolution of the vacuum cavity and the surrounding fluid distribution, emerging after a central explosion, thereby showing the potential of expansion–free condition for the study of that kind of problems. This study complements a previously published work where modeling of the evolution of such kind of systems was achieved through a different kinematical condition.

Charged anisotropic compact stars in Logarithmic-Corrected R2 gravity

2020 ◽  
Vol 35 (04) ◽  
pp. 2050013 ◽  
Author(s):  
M. Farasat Shamir ◽  
I. Fayyaz
Keyword(s):  
Energy Density ◽  
Electric Charge ◽  
Graphical Representation ◽  
Strong Electric Field ◽  
Compact Star ◽  
Compact Stars ◽  
Fluid Distribution ◽  
Anisotropic Fluid ◽  
Distribution Factor ◽  
Field Equations

We consider [Formula: see text] corrected model, i.e. [Formula: see text], where [Formula: see text] is the Ricci scalar and [Formula: see text], [Formula: see text] are arbitrary constant values, to investigate some of the interior configurations of static anisotropic spherical charged stellar structures. The existence of electric charge and a strong electric field confirms due to the higher values of pressure distribution and energy density of the matter inside the stars. Furthermore, for compact star configurations, we also consider the simplified MIT bag model equation of state (EoS) given by [Formula: see text], where [Formula: see text] is radial pressure, [Formula: see text] is energy density and [Formula: see text] is bag constant. This approach allows to find electric charge from the Einstein–Maxwell field equations. We have extensively discussed the behavior of the electric charge and anisotropic fluid distribution factor for five different values of [Formula: see text]. Interestingly, it is noticed during this study, for smaller values of [Formula: see text] we get intensity in electric charge. The Tolman–Oppenheimer–Volkoff equation (TOV), is modified in order to carry electric charge. In particular, we model the compact star candidates SAXJ 1808.4–3658 and Vela X-1 and give graphical representation of some important properties such as equilibrium condition, mass-radius ratio and surface redshift. In the end, our calculated solutions provide strong evidences for more realistic and viable charged stellar model.

scholarly journals Cylindrically Symmetric, Asymptotically Flat, Petrov Type D Spacetime with a Naked Curvature Singularity and Matter Collapse

2017 ◽  
Vol 2017 ◽  
pp. 1-6 ◽  
Author(s):  
Faizuddin Ahmed
Keyword(s):  
Cosmic Time ◽  
Petrov Type ◽  
Energy Conditions ◽  
Anisotropic Fluid ◽  
Curvature Singularity ◽  
Field Equations ◽  
Asymptotically Flat ◽  
Type D ◽  
Cylindrically Symmetric ◽  
Petrov Type D

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.

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