Variations in the expansion and shear scalars for dissipative fluids

2018 ◽  
Vol 33 (13) ◽  
pp. 1850076 ◽  
Author(s):  
A. Akram ◽  
S. Ahmad ◽  
A. Rehman Jami ◽  
M. Sufyan ◽  
U. Zahid
Keyword(s):  
Dust Cloud ◽  
Mass Function ◽  
Riemann Tensor ◽  
Spherical System ◽  
Structure Scalars ◽  
Specific Configuration ◽  
Dynamical Features ◽  
Weyl Scalar ◽  
Inhomogeneity Factor

This work is devoted to the study of some dynamical features of spherical relativistic locally anisotropic stellar geometry in f(R) gravity. In this paper, a specific configuration of tanh f(R) cosmic model has been taken into account. The mass function through technique introduced by Misner–Sharp has been formulated and with the help of it, various fruitful relations are derived. After orthogonal decomposition of the Riemann tensor, the tanh modified structure scalars are calculated. The role of these tanh modified structure scalars (MSS) has been discussed through shear, expansion as well as Weyl scalar differential equations. The inhomogeneity factor has also been explored for the case of radiating viscous locally anisotropic spherical system and spherical dust cloud with and without constant Ricci scalar corrections.

Role of modified scalar variables in the modeling of spherical fluids

2018 ◽  
Vol 15 (08) ◽  
pp. 1850140 ◽  
Author(s):  
A. Akram ◽  
A. Rehman Jami ◽  
S. Ahmad ◽  
M. Sufyan ◽  
R. Munir
Keyword(s):  
Degrees Of Freedom ◽  
Dust Cloud ◽  
Mass Function ◽  
Riemann Tensor ◽  
Ricci Scalar ◽  
Structure Scalars ◽  
Specific Distribution ◽  
Scalar Matter ◽  
Symmetric Geometry

The aim of this work is to analyze the role of shear evolution equation in the modeling of relativistic spheres in [Formula: see text] gravity. We assume that non-static diagonally symmetric geometry is coupled with dissipative anisotropic viscous fluid distributions in the presence of [Formula: see text] dark source terms. A specific distribution of [Formula: see text] cosmic model has been assumed and the spherical mass function through generic formula introduced by Misner-Sharp has been formulated. Some very important relations regarding Weyl scalar, matter variables and mass functions are being computed. After decomposing orthogonally the Riemann tensor, some scalar variables in the presence of [Formula: see text] extra degrees of freedom are calculated. The effects of the polynomial modified structure scalars in the modeling of through Weyl, shear, expansion scalar differential equations are investigated. The energy density irregularity factor has been calculated for both anisotropic radiating viscous with varying Ricci scalar and for dust cloud with present Ricci scalar corrections.

Role of structure scalars on viscous and heat conducting spherical systems in f(R,T) gravity

2017 ◽  
Vol 26 (14) ◽  
pp. 1750155 ◽  
Author(s):  
T. Hussain ◽  
M. Khurshudyan ◽  
S. Ahmed ◽  
As. Khurshudyan
Keyword(s):  
Evolution Equations ◽  
Energy Momentum Tensor ◽  
Gravitational Theory ◽  
Riemann Tensor ◽  
Momentum Tensor ◽  
Compact Objects ◽  
Heat Conducting ◽  
Structure Scalars ◽  
Dynamical Features

In this paper, we analyze some dynamical features of spherical celestial objects through structure scalars in [Formula: see text] gravitational theory, where [Formula: see text] and [Formula: see text] are the Ricci scalar and the trace of energy–momentum tensor, respectively. In this framework, we consider our relativistic geometry to be spherical in shape filled with radiating viscous and shearing fluid content. We formulate extended version of structure scalars by orthogonal decomposition of the Riemann tensor with and without constant [Formula: see text] and [Formula: see text] backgrounds. We discuss the effects of dark source corrections on the construction of expansion and shear evolution equations via scalar variables. It is inferred that like general relativity, one can investigate the evolutionary stages of stellar compact objects with the help of extended scalar parameters.

Shear and expansion evolution for dissipative fluids

2018 ◽  
Vol 33 (20) ◽  
pp. 1850111 ◽  
Author(s):  
S. Ahmad ◽  
A. Rehman Jami ◽  
Z. Aas
Keyword(s):  
Degrees Of Freedom ◽  
Dust Cloud ◽  
Mass Function ◽  
Riemann Tensor ◽  
Ricci Scalar ◽  
Structure Scalars ◽  
Specific Distribution ◽  
Scalar Matter ◽  
Symmetric Geometry ◽  
Density Irregularity

The aim of this work is to analyze the role of shear evolution equation in the modeling of relativistic spheres in f(R) gravity. We assume that non-static diagonally symmetric geometry is coupled with dissipative anisotropic viscous fluid distributions in the presence of f(R) dark source terms. A specific distribution of f(R) cosmic model has been assumed and the spherical mass function through generic formula introduced by Misner–Sharp has been formulated. Some very important relations regarding Weyl scalar, matter variables and mass functions are being computed. After decomposing orthogonally the Riemann tensor, some scalar variables in the presence of f(R) extra degrees of freedom are calculated. The effects of the three parametric modified structure scalars in the modeling of Weyl, shear, expansion scalar differential equations are investigated. The energy density irregularity factor has been calculated for both anisotropic radiating viscous with varying Ricci scalar and dust cloud with present Ricci scalar corrections.

scholarly journals Complexity of dynamical sphere in self-interacting Brans–Dicke gravity

2020 ◽  
Vol 80 (12) ◽  
Author(s):  
M. Sharif ◽  
Amal Majid
Keyword(s):  
Scalar Field ◽  
Riemann Tensor ◽  
Dissipative Systems ◽  
Anisotropic Pressure ◽  
Massive Scalar ◽  
Initial State ◽  
Spherical System ◽  
Massive Scalar Field ◽  
Structure Scalars ◽  
Definition Of

AbstractThis paper aims to derive a definition of complexity for a dynamic spherical system in the background of self-interacting Brans–Dicke gravity. We measure complexity of the structure in terms of inhomogeneous energy density, anisotropic pressure and massive scalar field. For this purpose, we formulate structure scalars by orthogonally splitting the Riemann tensor. We show that self-gravitating models collapsing homologously follow the simplest mode of evolution. Furthermore, we demonstrate the effect of scalar field on the complexity and evolution of non-dissipative as well as dissipative systems. The criteria under which the system deviates from the initial state of zero complexity is also discussed. It is concluded that complexity of the sphere increases in self-interacting Brans–Dicke gravity because the homologous model is not shear-free.

Complexity factor for self-gravitating system in modified Gauss–Bonnet gravity

2019 ◽  
Vol 34 (32) ◽  
pp. 1950210
Author(s):  
M. Sharif ◽  
Amal Majid ◽  
M. M. M. Nasir
Keyword(s):  
Mass Function ◽  
Riemann Tensor ◽  
Matter Distribution ◽  
Field Equations ◽  
Bonnet Gravity ◽  
Fundamental Properties ◽  
Structure Scalars ◽  
System A ◽  
Static Sphere

In this paper, we develop a complexity factor for static sphere in modified Gauss–Bonnet gravity with anisotropic and nonhomogeneous configuration. We use the field equations as well as equation of continuity to derive expressions for mass function in [Formula: see text] gravity. The Riemann tensor is split using Bel’s approach to formulate structure scalars that exhibit fundamental properties of the system. A complexity factor is developed on the basis of these scalars and the condition of vanishing complexity is used to obtain solutions of two different models. It is observed that modified terms increase complexity of the matter distribution.

Stellar systems and structure scalars

2019 ◽  
Vol 97 (5) ◽  
pp. 465-471 ◽  
Author(s):  
S. Ahmad ◽  
A. Rehman Jami ◽  
I. Ahmad ◽  
H. Sadia
Keyword(s):  
Riemann Tensor ◽  
Matter Content ◽  
Anisotropic Pressure ◽  
Energy Tensor ◽  
Spherically Symmetric ◽  
Structure Scalars ◽  
Tidal Forces ◽  
Stress Energy ◽  
Symmetric Geometry

The work is devoted to analyzing the effects of dark source polynomial curvature corrections in the mathematical modeling of radiating stars. In this scenario, we have used a particular f(R, T) model and consider the spherically symmetric geometry of relativistic interior. We assumed that our geometry is coupled with anisotropic shearing matter distribution undergoing radiating epoch with free streaming and diffusion approximation. We have calculated spherically symmetric total matter content with the help of Misner–Sharp formalism. A particular relation among anisotropic pressure, shearing viscosity, radiating parameters, energy density, and tidal forces is obtained. We then expressed this equation with the help of f(R, T) structure scalar, the scalar obtained by orthogonal decomposition of the Riemann tensor. The role of the logarithmic Ricci and trace of stress–energy tensor terms are also observed through Weyl scalar, shear, expansion scalar differential equations.

scholarly journals Simulations of the IMF in Clusters

2010 ◽  
Vol 6 (S270) ◽  
pp. 151-158
Author(s):  
Ralph E. Pudritz
Keyword(s):  
Equations Of State ◽  
Stellar Dynamics ◽  
Mass Function ◽  
Initial Mass Function ◽  
Core Mass ◽  
Numerical Work ◽  
Computational Approaches ◽  
The Core ◽  
The Imf

AbstractWe review computational approaches to understanding the origin of the Initial Mass Function (IMF) during the formation of star clusters. We examine the role of turbulence, gravity and accretion, equations of state, and magnetic fields in producing the distribution of core masses - the Core Mass Function (CMF). Observations show that the CMF is similar in form to the IMF. We focus on feedback processes such as stellar dynamics, radiation, and outflows can reduce the accreted mass to give rise to the IMF. Numerical work suggests that filamentary accretion may play a key role in the origin of the IMF.

Complexity factors for static axial system in self-interacting Brans–Dicke gravity

2019 ◽  
Vol 16 (11) ◽  
pp. 1950174 ◽  
Author(s):  
M. Sharif ◽  
Amal Majid
Keyword(s):  
Scalar Field ◽  
Evolution Equations ◽  
Riemann Tensor ◽  
Additional Source ◽  
Bianchi Identities ◽  
Structure Scalars ◽  
Physical Attributes ◽  
Physical Features ◽  
Axial System

This paper explores the physical attributes of a static axial source that induce complexity within the fluid in the background of self-interacting Brans–Dicke theory. Bel’s approach is used to split the Riemann tensor and construct structure scalars that involve physical features of the fluid in the presence of scalar field. Using the evolution equations derived from Bianchi identities as well as structure scalars, five complexity factors are identified which include constraints on the scalar field. Finally, the conditions of vanishing complexity are used to present solutions for an anisotropic inhomogeneous spheroid. It is concluded that scalar field is an additional source of complexity.

scholarly journals Karmarkar scalar condition

2020 ◽  
Vol 80 (2) ◽  
Author(s):  
J. Ospino ◽  
L. A. Núñez
Keyword(s):  
Differential Equation ◽  
Energy Density ◽  
Density Profile ◽  
Riemann Tensor ◽  
Orthogonal Decomposition ◽  
Algebraic Relation ◽  
Structure Scalars ◽  
Physical Variables ◽  
Adiabatic Case ◽  
Dissipative Dynamic

AbstractIn this work we present the Karmarkar condition in terms of the structure scalars obtained from the orthogonal decomposition of the Riemann tensor. This new expression becomes an algebraic relation among the physical variables, and not a differential equation between the metric coefficients. By using the Karmarkar scalar condition we implement a method to obtain all possible embedding class I static spherical solutions, provided the energy density profile is given. We also analyse the dynamic adiabatic case and show the incompatibility of the Karmarkar condition with several commonly assumed simplifications to the study of gravitational collapse. Finally, we consider the dissipative dynamic Karmarkar collapse and find a new solution family.

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