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.

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.

Gaussian distributed wormholes exhibiting conformal motion in f(T) gravity

2019 ◽  
Vol 16 (09) ◽  
pp. 1950143 ◽  
Author(s):  
G. Mustafa ◽  
Saira Waheed ◽  
M. Zubair ◽  
T. Xia
Keyword(s):  
String Theory ◽  
Energy Density ◽  
Analytic Solution ◽  
Numerical Approach ◽  
Anisotropic Fluid ◽  
Matter Distribution ◽  
Field Equations ◽  
Conformal Motion ◽  
Free Parameters ◽  
The Stability

This paper investigates the possibility of static spherical symmetric wormholes existence exhibiting conformal motion in a generalized teleparallel formulation, namely [Formula: see text] gravity. For this purpose, we assume the matter distribution as anisotropic fluid with energy density of Gaussian distribution, a well-known non-commutative aspect of string theory. By using non-diagonal tetrad components in the torsional formulation, we consider three interesting viable models of [Formula: see text]. In each case, due to the complexity of the resulting field equations, it is seen that the analytic solution is difficult to find. Thus the feasible and realistic wormholes are acquired using numerical approach by fixing the involved free parameters suitably. Furthermore, we investigate the stability of these wormhole solutions graphically and it is shown that the obtained wormhole solutions are physically stable in all cases.

scholarly journals EXACT NONSPHERICAL RELATIVISTIC STAR

2010 ◽  
Vol 25 (12) ◽  
pp. 2573-2583
Author(s):  
SUSHANT G. GHOSH ◽  
D. W. DESHKAR
Keyword(s):  
Cosmological Constant ◽  
Analytical Solutions ◽  
De Sitter Space ◽  
De Sitter ◽  
Einstein’S Field Equations ◽  
Field Equations ◽  
Relativistic Star ◽  
Plane Symmetric ◽  
Negative Cosmological Constant ◽  
Einstein's Equation

Einstein's equation with a negative cosmological constant admit solutions which are asymptotically anti-de Sitter. We obtain Vaidya-like solutions to include both a null fluid and a string fluid in nonspherical (plane symmetric and cylindrical symmetric) anti-de Sitter space–times. Assuming that string fluid diffuse, we find analytical solutions to Einstein's field equations. Thus we extend the approach proposed by Glass and Krisch to nonspherical space–times with a negative cosmological constant. Some other exacts solutions are also presented and discussed.

scholarly journals Does the Cosmological Expansion Change Local Dynamics?

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1417
Author(s):  
Marcelo Schiffer
Keyword(s):  
Dark Matter ◽  
Modified Gravity ◽  
Hubble Constant ◽  
Matter Content ◽  
Matter Distribution ◽  
Present Value ◽  
Field Equations ◽  
Local Dynamics ◽  
Cosmological Expansion ◽  
Modified Gravity Theories

It is a well-known fact that the Newtonian description of dynamics within Galaxies for its known matter content is in disagreement with the observations as the acceleration approaches a0≈1.2×10−10 m/s2 (slighter larger for clusters). Both the Dark Matter scenario and Modified Gravity Theories (MGT) fail to explain the existence of such an acceleration scale. Motivated by the closeness of the acceleration scale and the Hubble constant cH0≈10−9 h m/s2, we are led to analyze whether this coincidence might have a Cosmological origin for scalar-tensor and spinor-tensor theories by performing detailed calculations for perturbations that represent the local matter distribution on the top of the cosmological background. Then, we solve the field equations for these perturbations in a power series in the present value of the Hubble constant. As we shall see, for both theories, the power expansion contains only even powers in the Hubble constant, a fact that renders the cosmological expansion irrelevant for the local dynamics.

RADIATING COLLAPSE WITH VANISHING WEYL STRESSES

2005 ◽  
Vol 14 (03n04) ◽  
pp. 667-676 ◽  
Author(s):  
S. D. MAHARAJ ◽  
M. GOVENDER
Keyword(s):  
Irreversible Thermodynamics ◽  
Temperature Profiles ◽  
Junction Conditions ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Extended Irreversible Thermodynamics ◽  
Recent Approach ◽  
Dust Solution ◽  
Limiting Case

In a recent approach in modeling a radiating relativistic star undergoing gravitational collapse the role of the Weyl stresses was emphasized. It is possible to generate a model which is physically reasonable by approximately solving the junction conditions at the boundary of the star. In this paper we demonstrate that it is possible to solve the Einstein field equations and the junction conditions exactly. This exact solution contains the Friedmann dust solution as a limiting case. We briefly consider the radiative transfer within the framework of extended irreversible thermodynamics and show that relaxational effects significantly alter the temperature profiles.

Phase space correspondence between Jordan and Einstein frames

2021 ◽  
pp. 2150087
Author(s):  
Amin Salehi
Keyword(s):  
Phase Space ◽  
Critical Point ◽  
Critical Points ◽  
Dynamical Behavior ◽  
Cosmological Parameters ◽  
Jordan Frame ◽  
Field Equations ◽  
Theories Of Gravity ◽  
The Stability ◽  
Jordan And Einstein Frames

Scalar–tensor theories of gravity can be formulated in the Einstein frame or in the Jordan frame (JF) which are related with each other by conformal transformations. Although the two frames describe the same physics and are equivalent, the stability of the field equations in the two frames is not the same. Here, we implement dynamical system and phase space approach as a robustness tool to investigate this issue. We concentrate on the Brans–Dicke theory in a Friedmann–Lemaitre–Robertson–Walker universe, but the results can easily be generalized. Our analysis shows that while there is a one-to-one correspondence between critical points in two frames and each critical point in one frame is mapped to its corresponds in another frame, however, stability of a critical point in one frame does not guarantee the stability in another frame. Hence, an unstable point in one frame may be mapped to a stable point in another frame. All trajectories between two critical points in phase space in one frame are different from their corresponding in other ones. This indicates that the dynamical behavior of variables and cosmological parameters is different in two frames. Hence, for those features of the study, which focus on observational measurements, we must use the JF where experimental data have their usual interpretation.

Impact of f(R,T) gravity in evolution of charged viscous fluids

2021 ◽  
Vol 30 (04) ◽  
pp. 2150027
Author(s):  
I. Noureen ◽  
Usman-ul-Haq ◽  
S. A. Mardan
Keyword(s):  
Stability Analysis ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Viscous Fluids ◽  
Fluid Distribution ◽  
Perturbation Scheme ◽  
Field Equations ◽  
Dynamical Equations ◽  
Stability Of Stars ◽  
The Stability

In this work, the evolution of spherically symmetric charged anisotropic viscous fluids is discussed in framework of [Formula: see text] gravity. In order to conduct the analysis, modified Einstein Maxwell field equations are constructed. Nonzero divergence of modified energy momentum tensor is taken that implicates dynamical equations. The perturbation scheme is applied to dynamical equations for stability analysis. The stability analysis is carried out in Newtonian and post-Newtonian limits. It is observed that charge, fluid distribution, electromagnetic field, viscosity and mass of the celestial objects greatly affect the collapsing process as well as stability of stars.

scholarly journals On the exact and numerical solutions to a nonlinear model arising in mathematical biology

2018 ◽  
Vol 22 ◽  
pp. 01061 ◽  
Author(s):  
Asif Yokus ◽  
Tukur Abdulkadir Sulaiman ◽  
Haci Mehmet Baskonus ◽  
Sibel Pasali Atmaca
Keyword(s):  
Analytical Solutions ◽  
Numerical Solutions ◽  
Soliton Solutions ◽  
Hyperbolic Function ◽  
Von Neumann ◽  
Convection Diffusion Equation ◽  
Wolfram Mathematica ◽  
Forward Difference ◽  
Von Neumann Analysis ◽  
The Stability

This study acquires the exact and numerical approximations of a reaction-convection-diffusion equation arising in mathematical bi- ology namely; Murry equation through its analytical solutions obtained by using a mathematical approach; the modified exp(-Ψ(η))-expansion function method. We successfully obtained the kink-type and singular soliton solutions with the hyperbolic function structure to this equa- tion. We performed the numerical simulations (3D and 2D) of the obtained analytical solutions under suitable values of parameters. We obtained the approximate numerical and exact solutions to this equa- tion by utilizing the finite forward difference scheme by taking one of the obtained analytical solutions into consideration. We investigate the stability of the finite forward difference method with the equation through the Fourier-Von Neumann analysis. We present the L2 and L∞ error norms of the approximations. The numerical and exact approx- imations are compared and the comparison is supported by a graphic plot. All the computations and the graphics plots in this study are car- ried out with help of the Matlab and Wolfram Mathematica softwares. Finally, we submit a comprehensive conclusion to this study.

New molecular insights into the stability of Ni–Pd hollow nanoparticles

2017 ◽  
Vol 4 (10) ◽  
pp. 1679-1690 ◽  
Author(s):  
Hamed Akbarzadeh ◽  
Esmat Mehrjouei ◽  
Amir Nasser Shamkhali ◽  
Mohsen Abbaspour ◽  
Sirous Salemi ◽  
...  
Keyword(s):  
Molecular Dynamics ◽  
Thermal Behavior ◽  
Molecular Dynamics Simulations ◽  
Structural Evolution ◽  
Hollow Nanoparticles ◽  
The Stability ◽  
Dynamics Simulations

Molecular dynamics simulations were used to investigate the structural evolution and thermal behavior of Ni–Pd hollow nanoparticles.

scholarly journals On the stability of Einstein universe in f(R, T, Rμν Tμν) gravity

2018 ◽  
Vol 33 (36) ◽  
pp. 1850216 ◽  
Author(s):  
M. Sharif ◽  
Arfa Waseem
Keyword(s):  
State Parameter ◽  
Big Bang ◽  
Graphical Analysis ◽  
Momentum Tensor ◽  
Field Equations ◽  
Einstein Universe ◽  
Existence And Stability ◽  
The Stability ◽  
The Big Bang ◽  
Big Bang Singularity

This paper investigates the existence and stability of Einstein universe in the context of f(R, T, Q) gravity, where Q = R[Formula: see text] T[Formula: see text]. Considering linear homogeneous perturbations around scale factor and energy density, we formulate static as well as perturbed field equations. We parametrize the stability regions corresponding to conserved as well as non-conserved energy–momentum tensor using linear equation of state parameter for particular models of this gravity. The graphical analysis concludes that for a suitable choice of parameters, stable regions of the Einstein universe are obtained which indicates that the big bang singularity can be avoided successfully by the emergent mechanism in non-minimal matter-curvature coupled gravity.

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