scholarly journals Collapse and expansion of plane symmetric charged anisotropic source

2017 ◽  
Vol 95 (2) ◽  
pp. 114-118 ◽  
Author(s):  
G. Abbas ◽  
S.M. Shah ◽  
M. Zubair
Keyword(s):  
Apparent Horizon ◽  
Field Equations ◽  
Plane Symmetric ◽  
Radial Heat ◽  
Symmetric Source ◽  
New Form ◽  
Metric Functions ◽  
Static Plane ◽  
Radial Heat Flux ◽  
Anisotropic Source

In this paper, we have investigated the final evolutionary stages of charged non-static plane symmetric anisotropic source. To this end, we have solved the Einstein–Maxwell field equations with the charged plane symmetric source. We have found that vanishing of radial heat flux in the gravitating source provides the parametric form of the metric functions. The new form of the metric functions can generate a class of physically acceptable solutions depending on the choice parameter. These solutions may be classified as expanding or collapsing solutions with the particular values of generating parameter. The gravitational collapse in this case ends with the formation of single apparent horizon while there exists two such horizons in the case of charged spherical anisotropic source.

scholarly journals Some analytic models of plane symmetric radiating collapse

2017 ◽  
Vol 95 (1) ◽  
pp. 65-68 ◽  
Author(s):  
G. Abbas ◽  
Hassan Shah ◽  
Zahid Ahmad
Keyword(s):  
Thermal Behavior ◽  
Analytical Solutions ◽  
Adiabatic Index ◽  
Junction Conditions ◽  
Matter Distribution ◽  
Field Equations ◽  
Plane Symmetric ◽  
Symmetric Source ◽  
The Stability ◽  
Analytic Models

This paper deals with the analytical solutions of the field equations in the presence of radiating plane symmetric source. For this purpose we have solved the field equations as well as junction conditions by imposing the conformal flatness conditions. The effective adiabatic index (that determines the stability of the system) has been calculated for the present radiating source. It has been found that effective adiabatic index remains invariant throughout the matter distribution. To study the thermal behavior of the source, we have discussed the thermal profile of the source and found that in the absence of dissipation from the system the temperature of the system remains constant.

A study of energy conditions in static plane symmetric space–times via homothetic symmetries

2019 ◽  
Vol 34 (35) ◽  
pp. 1950238
Author(s):  
Tahir Hussain ◽  
Uzma Nasib ◽  
Muhammad Farhan ◽  
Ashfaque H. Bokhari
Keyword(s):  
Symmetric Space ◽  
Vector Fields ◽  
Momentum Tensor ◽  
Energy Conditions ◽  
Field Equations ◽  
New Approach ◽  
Plane Symmetric ◽  
Homothetic Vector ◽  
Integration Techniques ◽  
Static Plane

The aim of this study is twofold. First, we use a new approach to study the homothetic vector fields (HVFs) of static plane symmetric space–times by an algorithm which we have developed using the Maple platform. The interesting feature of this algorithm is that it provides the most general form of metrics admitting HVFs as compared to those obtained in an earlier study where direct integration techniques were used. Second, the obtained metrics are used in Einstein’s field equations to compute the energy–momentum tensor and it is shown how the parameters involved in the obtained space–time metrics are associated with certain important energy conditions.

Conformal vector fields in proper non-static plane symmetric spacetimes in f(R) gravity

2020 ◽  
Vol 17 (05) ◽  
pp. 2050077 ◽  
Author(s):  
Fiaz Hussain ◽  
Ghulam Shabbir ◽  
F. M. Mahomed ◽  
Muhammad Ramzan
Keyword(s):  
Vector Fields ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Plane Symmetric ◽  
Symmetric Spacetimes ◽  
Integration Approach ◽  
Conformal Vector ◽  
Conformal Vector Fields ◽  
Theory Of Gravity ◽  
Static Plane

Nonstatic plane symmetric spacetimes are considered to study conformal vector fields (VFs) in the [Formula: see text] theory of gravity. Firstly, we investigate some proper nonstatic plane symmetric spacetimes by solving the Einstein field equations (EFEs) in the [Formula: see text] theory of gravity using algebraic techniques. Secondly, we find CVFs of the obtained spacetimes by means of the direct integration approach. There exist seven cases. Studying each case in detail, we find that the CVFs are of dimension three, five, six and fifteen.

Classification of non-conformally flat static plane symmetric perfect fluid solutions via proper conformal vector fields in f(T) gravity

2020 ◽  
Vol 17 (14) ◽  
pp. 2050218
Author(s):  
Murtaza Ali ◽  
Fiaz Hussain ◽  
Ghulam Shabbir ◽  
S. F. Hussain ◽  
Muhammad Ramzan
Keyword(s):  
Perfect Fluid ◽  
Vector Fields ◽  
Killing Vector ◽  
Flat Space ◽  
Conformally Flat ◽  
Field Equations ◽  
Plane Symmetric ◽  
Conformal Vector ◽  
Conformal Vector Fields ◽  
Static Plane

The aim of this paper is to classify non-conformally flat static plane symmetric (SPS) perfect fluid solutions via proper conformal vector fields (CVFs) in [Formula: see text] gravity. For this purpose, first we explore some SPS perfect fluid solutions of the Einstein field equations (EFEs) in [Formula: see text] gravity. Second, we utilize these solutions to find proper CVFs. In this study, we found 16 cases. A detailed study of each case reveals that in three of these cases, the space-times admit proper CVFs whereas in the rest of the cases, either the space-times become conformally flat or they admit proper homothetic vector fields (HVFs) or Killing vector fields (KVFs). The dimension of CVFs for non-conformally flat space-times in [Formula: see text] gravity is four, five or six.

scholarly journals Static plane-symmetric solution of a scalar-tensor theory of gravitation

1983 ◽  
Vol 24 (3) ◽  
pp. 339-342 ◽  
Author(s):  
D. R. K. Reddy ◽  
V. U. M. Rao
Keyword(s):  
Exact Solution ◽  
Symmetric Solution ◽  
Empty Space ◽  
Vacuum Field ◽  
Scalar Tensor Theory ◽  
Field Equations ◽  
Plane Symmetric ◽  
Tensor Theory ◽  
Theory Of Gravitation ◽  
Static Plane

AbstractVacuum field equations in a scalar-tensor theory of gravitation, proposed by Ross, are obtained with the aid of a static plane-symmetric metric. A closed form exact solution to the field equations in this theory is presented which can be considered as an analogue of Taub's empty space-time in Einstein's theory.

Expansion and collapse of spherical source with cosmological constant

2019 ◽  
Vol 34 (05) ◽  
pp. 1950042
Author(s):  
G. Abbas ◽  
Shahid Qaisar ◽  
Hamood Ur Rehman ◽  
M. Younas
Keyword(s):  
Cosmological Constant ◽  
Mass Function ◽  
Parametric Form ◽  
De Sitter ◽  
Field Equations ◽  
Spherical Source ◽  
Expansion Scalar ◽  
Radial Heat ◽  
Metric Functions ◽  
Metric Function

In this research paper, we address the issues of expansion and gravitational collapse of anisotropic spherical source in the presence of cosmological constant. For this purpose, we have solved the Einstein field equations with gravitating source and cosmological constant. The absence of radial heat flux in the gravitating source provide the parametric form of two-metric functions in terms of a single-metric function. The expansion scalar and the mass function of the gravitating source is evaluated for the given metric. The trapping condition is applied to mass function which implies the existence of horizons, like the horizons of Schwarzschild de-Sitter black holes. The trapping condition provides the parametric form of the unknown metric function. The value of expansion scalar has been analyzed in detail to see its positivity and negativity, which correspond to expansion and collapse, respectively. So, the values of parameter [Formula: see text] for which expansion scalar is positive have been used to analyze the other physical variables including density, pressures and anisotropy. The same quantities have been evaluated for the values of [Formula: see text] that result in the negative values of expansion scalar leading to collapse. The effects of positive cosmological constant have been noted in both expansion and collapse solutions. Due to the presence of cosmological constant after collapse, there would occur inner and outer horizons or a unique horizon depending on the value of mass of the gravitating source.

scholarly journals PLANE SYMMETRIC SOLUTIONS IN f(R) GRAVITY

2010 ◽  
Vol 25 (15) ◽  
pp. 1281-1288 ◽  
Author(s):  
M. SHARIF ◽  
M. FARASAT SHAMIR
Keyword(s):  
General Relativity ◽  
Scalar Curvature ◽  
Constant Scalar Curvature ◽  
Modified Theories Of Gravity ◽  
Field Equations ◽  
Plane Symmetric ◽  
Symmetric Vacuum ◽  
Theories Of Gravity ◽  
Static Plane ◽  
Vacuum Solutions

The modified theories of gravity, especially the f(R) theory, have attracted much attention in recent years. In this context, we explore static plane symmetric vacuum solutions using the metric approach of this theory. The field equations are solved using the assumption of constant scalar curvature which may be zero or nonzero. We have found a total of three plane symmetric solutions. The correspondence of these solutions with the well-known solutions in General Relativity is given.

scholarly journals RADIATING GRAVITATIONAL COLLAPSE WITH SHEARING MOTION AND BULK VISCOSITY REVISITED

2010 ◽  
Vol 19 (11) ◽  
pp. 1797-1822 ◽  
Author(s):  
G. PINHEIRO ◽  
R. CHAN
Keyword(s):  
Black Hole ◽  
Bulk Viscosity ◽  
Apparent Horizon ◽  
Adiabatic Index ◽  
Time Dependent ◽  
Previous Model ◽  
Anisotropic Fluid ◽  
Formation Condition ◽  
Radial Heat ◽  
Metric Functions

A new model is proposed to collapsing stars consisting of an anisotropic fluid with bulk viscosity, radial heat flow and outgoing radiation. In a previous paper one of us has introduced a time-dependent function into the grr, besides the time-dependent metric functions gθθ and gϕϕ. The aim of this work is to generalize this previous model by introducing bulk viscosity and comparing it to the non-viscous collapse. The behavior of the density, pressure, mass, luminosity and the effective adiabatic index is analyzed. Our work is also compared to the case of a collapsing fluid with bulk viscosity of another previous model, for a star with 6 M⊙. The pressure of the star, at the beginning of the collapse, is isotropic, but due to the presence of the bulk viscosity the pressure becomes more and more anisotropic. The black hole is never formed because the apparent horizon formation condition is never satisfied, in contrast to the previous model where a black hole is formed. An observer at infinity sees a radial point source radiating exponentially until it reaches the time of maximum luminosity, and suddenly the star turns off. This is in contrast to the former model where the luminosity also increases exponentially, reaching a maximum and decreases thereafter until the formation of the black hole. The effective adiabatic index diminishes due to the bulk viscosity, thus increasing the instability of the system, in both models, in the former paper as well as in this work.

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