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.

scholarly journals Generalised radiating fields in Einstein–Gauss–Bonnet gravity

2020 ◽  
Vol 80 (10) ◽  
Author(s):  
Byron P. Brassel ◽  
Sunil D. Maharaj
Keyword(s):  
Mass Function ◽  
Spherically Symmetric ◽  
Diffusive Transport ◽  
Mass Energy ◽  
Matter Distribution ◽  
Field Equations ◽  
Bonnet Gravity ◽  
Spacetime Manifold ◽  
Specific Equation ◽  
Higher Order Curvature Corrections

AbstractA five-dimensional spherically symmetric generalised radiating field is studied in Einstein–Gauss–Bonnet gravity. We assume the matter distribution is an extended Vaidya-like source and the resulting Einstein–Gauss–Bonnet field equations are solved for the matter variables and mass function. The evolution of the mass, energy density and pressure are then studied within the spacetime manifold. The effects of the higher order curvature corrections of Einstein–Gauss–Bonnet gravity are prevalent in the analysis of the mass function when compared to general relativity. The effects of diffusive transport are then considered and we derive the specific equation for which diffusive behaviour is possible. Gravitational collapse is then considered and we show that collapse ends with a weak and conical singularity for the generalised source, which is not the case in Einstein gravity.

scholarly journals Influence of modification of gravity on the complexity factor of static spherical structures

2020 ◽  
Vol 495 (4) ◽  
pp. 4334-4346
Author(s):  
Z Yousaf ◽  
Maxim Yu Khlopov ◽  
M Z Bhatti ◽  
T Naseer
Keyword(s):  
Gravitational Theory ◽  
Momentum Tensor ◽  
Matter Distribution ◽  
Field Equations ◽  
Riemann Curvature Tensor ◽  
Structure Scalars ◽  
Pressure Anisotropy ◽  
Spherical Structures ◽  
Energy Density Inhomogeneity ◽  
Definition Of

ABSTRACT The aim of this paper is to generalize the definition of complexity for the static self-gravitating structure in f (R, T, Q) gravitational theory, where R is the Ricci scalar, T is the trace part of energy–momentum tensor, and Q ≡ RαβT αβ. In this context, we have considered locally anisotropic spherical matter distribution and calculated field equations and conservation laws. After the orthogonal splitting of the Riemann curvature tensor, we found the corresponding complexity factor with the help of structure scalars. It is seen that the system may have zero complexity factor if the effects of energy density inhomogeneity and pressure anisotropy cancel the effects of each other. All of our results reduce to general relativity on assuming f (R, T, Q) = R condition.

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.

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.

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.

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.

DESITTER GAUGE THEORY OF GRAVITATION

2003 ◽  
Vol 14 (01) ◽  
pp. 41-48 ◽  
Author(s):  
G. ZET ◽  
V. MANTA ◽  
S. BABETI
Keyword(s):  
Gauge Theory ◽  
Riemann Tensor ◽  
Space Time ◽  
Point Of View ◽  
Field Equations ◽  
Minkowski Space Time ◽  
Strength Tensor ◽  
Group A ◽  
Theory Of Gravitation ◽  
Tensor Formula

A deSitter gauge theory of gravitation over a spherical symmetric Minkowski space–time is developed. The "passive" point of view is adapted, i.e., the space–time coordinates are not affected by group transformations; only the fields change under the action of the symmetry group. A particular ansatz for the gauge fields is chosen and the components of the strength tensor are computed. An analytical solution of Schwarzschild–deSitter type is obtained in the case of null torsion. It is concluded that the deSitter group can be considered as a "passive" gauge symmetry for gravitation. Because of their complexity, all the calculations, inclusive of the integration of the field equations, are performed using an analytical program conceived in GRTensorII for MapleV. The program allows one to compute (without using a metric) the strength tensor [Formula: see text], Riemann tensor [Formula: see text], Ricci tensor [Formula: see text], curvature scalar [Formula: see text], field equations, and the integration of these equations.

A spatially homogeneous gravitational field

1966 ◽  
Vol 62 (1) ◽  
pp. 87-89 ◽  
Author(s):  
V. Joseph
Keyword(s):  
Gravitational Field ◽  
Canonical Form ◽  
Riemann Tensor ◽  
Vacuum Field ◽  
Type I ◽  
Field Equations ◽  
Parameter Group ◽  
Spatially Homogeneous ◽  
Homogeneous Gravitational Field ◽  
Type V

AbstractA solution of Einstein's vacuum field equations, apparently new, is exhibited. The metric, which is homogeneous (that is, admits a three-parameter group of motions transitive on space-like hypersurfaces), belongs to Taub Type V. The canonical form of the Riemann tensor, which is of Petrov Type I, is determined.

Anisotropic compact stars model with generalized Bardeen–Hayward mass function

2021 ◽  
Vol 36 (26) ◽  
pp. 2150190
Author(s):  
Nayan Sarkar ◽  
Susmita Sarkar ◽  
Farook Rahaman ◽  
Ksh. Newton Singh
Keyword(s):  
Surface Density ◽  
Mass Function ◽  
Static Stability ◽  
Compact Stars ◽  
Energy Conditions ◽  
Causality Condition ◽  
Field Equations ◽  
Regular Black Hole ◽  
Bag Constant ◽  
Tov Equation

A new compact stars nonsingular model is presented with the generalized Bardeen–Hayward mass function. Generalized Bardeen–Hayward described the regular black hole, however, due to its regularity or nonsingular nature we were inspired to construct an anisotropic compact stars model. Along with the ansatz mass function, we coupled it with a linear equation of state (EoS) to find the solutions of field equations. Indeed, the new solutions are physically viable in all physical ground. The energy conditions and Tolman–Oppenheimer–Volkoff (TOV)-equation are well satisfied signifying that the mass distribution is physically possible and at equilibrium. Also, the static stability criterion, the causality condition and Abreu’s stability condition hold good and therefore configurations are physically static stable. The same condition is further supported by the condition that the adiabatic index, which is greater than the Newtonian limit, i.e. [Formula: see text]. It is also noticed that the bag constant [Formula: see text] is proportional to the surface density in our model.

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