scholarly journals GENERATING ANISOTROPIC FLUIDS FROM VACUUM ERNST EQUATIONS

2010 ◽  
Vol 19 (11) ◽  
pp. 1783-1795 ◽  
Author(s):  
STEFANO VIAGGIU
Keyword(s):  
Momentum Tensor ◽  
Energy Conditions ◽  
Coordinate Systems ◽  
Field Equations ◽  
Oblate Spheroidal ◽  
Basic Equations ◽  
Ernst Equations ◽  
Vacuum Solutions ◽  
Anisotropic Fluids ◽  
Spheroidal Coordinates

Starting with any stationary axisymmetric vacuum metric, we build anisotropic fluids. With the help of the Ernst method, the basic equations are derived together with the expression for the energy–momentum tensor and with the equation of state compatible with the field equations. The method is presented by using different coordinate systems: the cylindrical coordinates ρ, z and the oblate spheroidal ones. A class of interior solutions matching with stationary axisymmetric asymptotically flat vacuum solutions is found in oblate spheroidal coordinates. The solutions presented satisfy the three energy conditions.

scholarly journals Compact stars in f(ℛ,𝒢,𝒯 ) gravity

2021 ◽  
Vol 36 (24) ◽  
pp. 2150165
Author(s):  
M. Ilyas
Keyword(s):  
Test Particle ◽  
Gravitational Theory ◽  
Momentum Tensor ◽  
Conservation Equation ◽  
Compact Objects ◽  
Compact Stars ◽  
Energy Conditions ◽  
Field Equations ◽  
Physical Features ◽  
The Impact

This work is to introduce a new kind of modified gravitational theory, named as [Formula: see text] (also [Formula: see text]) gravity, where [Formula: see text] is the Ricci scalar, [Formula: see text] is Gauss–Bonnet invariant and [Formula: see text] is the trace of the energy–momentum tensor. With the help of different models in this gravity, we investigate some physical features of different relativistic compact stars. For this purpose, we develop the effectively modified field equations, conservation equation, and the equation of motion for test particle. Then, we check the impact of additional force (massive test particle followed by a nongeodesic line of geometry) on compact objects. Furthermore, we took three notable stars named as [Formula: see text], [Formula: see text] and [Formula: see text]. The physical behavior of the energy density, anisotropic pressures, different energy conditions, stability, anisotropy, and the equilibrium scenario of these strange compact stars are analyzed through various plots. Finally, we conclude that the energy conditions hold, and the core of these stars is so dense.

Study of gravitational decoupled anisotropic solution

2019 ◽  
Vol 28 (16) ◽  
pp. 2040004
Author(s):  
M. Sharif ◽  
Sobia Sadiq
Keyword(s):  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Energy Conditions ◽  
Spherically Symmetric ◽  
Anisotropic Model ◽  
Field Equations ◽  
Anisotropic Solution ◽  
Spherically Symmetric Solution ◽  
Gravitational Source ◽  
The Stability

This paper formulates the exact static anisotropic spherically symmetric solution of the field equations through gravitational decoupling. To accomplish this work, we add a new gravitational source in the energy–momentum tensor of a perfect fluid. The corresponding field equations, hydrostatic equilibrium equation as well as matching conditions are evaluated. We obtain the anisotropic model by extending the known Durgapal and Gehlot isotropic solution and examined the physical viability as well as the stability of the developed model. It is found that the system exhibits viable behavior for all fluid variables as well as energy conditions and the stability criterion is fulfilled.

Axial symmetry causality violating spacetime and the naked singularity

2018 ◽  
Vol 15 (09) ◽  
pp. 1850153 ◽  
Author(s):  
Faizuddin Ahmed
Keyword(s):  
Symmetry Axis ◽  
Energy Content ◽  
Naked Singularity ◽  
Energy Conditions ◽  
Field Equations ◽  
Closed Timelike Curves ◽  
Radiation Fields ◽  
Strong Curvature ◽  
Anisotropic Fluids ◽  
Matter Energy

A non-spherical solution of Einstein’s field equations, possessing a naked curvature singularity on the symmetry axis, satisfying the strong curvature condition, is presented. The spacetime admits closed timelike curves which appear after a certain instant of time in a causally well-behaved manner. The matter–energy content radiation fields, coupled with anisotropic fluids, obeying the energy conditions, diverge on the symmetry axis.

Exact wormholes solutions without exotic matter in f(R,T) gravity

2019 ◽  
Vol 16 (03) ◽  
pp. 1950046 ◽  
Author(s):  
M. Zubair ◽  
Rabia Saleem ◽  
Yasir Ahmad ◽  
G. Abbas
Keyword(s):  
Momentum Tensor ◽  
Exotic Matter ◽  
Gravity Models ◽  
Energy Conditions ◽  
Anisotropic Fluid ◽  
Energy Tensor ◽  
Field Equations ◽  
Stress Energy ◽  
Symmetric Geometry ◽  
The Stability

This paper is aimed to evaluate the existence of wormholes in viable [Formula: see text] gravity models (where [Formula: see text] is the scalar curvature and [Formula: see text] is the trace of stress–energy tensor of matter). The exact solutions for energy–momentum tensor components depending on different shapes and redshift functions are calculated without some additional constraints. To investigate this, we consider static spherically symmetric geometry with matter contents as anisotropic fluid and formulate the Einstein field equations for three different [Formula: see text] models. For each model, we derive expression for weak and null energy conditions and graphically analyzed its violation near the throat. It is really interesting that wormhole solutions do not require the presence of exotic matter — like that in general relativity. Finally, the stability of the solutions for each model is presented using equilibrium condition.

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.

On a Bianchi type-I space-time with bulk viscosity in f(R,T) gravity

2021 ◽  
Author(s):  
M. Koussour ◽  
M. Bennai
Keyword(s):  
Deceleration Parameter ◽  
Bianchi Type ◽  
Momentum Tensor ◽  
Energy Conditions ◽  
Type I ◽  
Field Equations ◽  
Bulk Fluid ◽  
Bianchi Type I ◽  
Deceleration Phase ◽  
Spatially Homogeneous

In this paper, we present a spatially homogeneous and anisotropic Bianchi type-I cosmological model with a viscous bulk fluid in [Formula: see text] gravity where [Formula: see text] and [Formula: see text] are the Ricci scalar and trace of the energy-momentum tensor, respectively. The field equations are solved explicitly using the hybrid law of the scale factor, which is related to the average Hubble parameter and gives a time-varying deceleration parameter (DP). We found the deceleration parameter describing two phases in the universe, the early deceleration phase [Formula: see text] and the current acceleration phase [Formula: see text]. We have calculated some physical and geometric properties and their graphs, whether in terms of time or redshift. Note that for our model, the bulk viscous pressure [Formula: see text] is negative and the energy density [Formula: see text] is positive. The energy conditions and the [Formula: see text] analysis for our spatially homogeneous and anisotropic Bianchi type-I model are also discussed.

scholarly journals Eigenfunction Expansions for the Stokes Flow Operators in the Inverted Oblate Coordinate System

2016 ◽  
Vol 2016 ◽  
pp. 1-6
Author(s):  
Maria Hadjinicolaou ◽  
Eleftherios Protopapas
Keyword(s):  
Coordinate System ◽  
Fluid Flows ◽  
Scalar Function ◽  
Order Partial Differential Equation ◽  
Coordinate Systems ◽  
Prolate Spheroidal ◽  
Spherical System ◽  
Oblate Spheroidal ◽  
Generalized Eigenfunctions ◽  
Spheroidal Coordinates

When studying axisymmetric particle fluid flows, a scalar function,ψ, is usually employed, which is called a stream function. It serves as a velocity potential and it can be used for the derivation of significant hydrodynamic quantities. The governing equation is a fourth-order partial differential equation; namely,E4ψ=0, whereE2is the Stokes irrotational operator andE4=E2∘E2is the Stokes bistream operator. As it is already known,E2ψ=0in some axisymmetric coordinate systems, such as the cylindrical, spherical, and spheroidal ones, separates variables, while in the inverted prolate spheroidal coordinate system, this equation acceptsR-separable solutions, as it was shown recently by the authors. Notably, the kernel space of the operatorE4does not decompose in a similar way, since it accepts separable solutions in cylindrical and spherical system of coordinates, whileE4ψ=0semiseparates variables in the spheroidal coordinate systems and itR-semiseparates variables in the inverted prolate spheroidal coordinates. In addition to these results, we show in the present work that in the inverted oblate spheroidal coordinates, the equationE′2ψ=0alsoR-separates variables and we derive the eigenfunctions of the Stokes operator in this particular coordinate system. Furthermore, we demonstrate that the equationE′4ψ=0  R-semiseparates variables. Since the generalized eigenfunctions ofE′2cannot be obtained in a closed form, we present a methodology through which we can derive the complete set of the generalized eigenfunctions ofE′2in the modified inverted oblate spheroidal coordinate system.

scholarly journals STUDY OF SELF-SUPERPOSABLE LIQUID IN OBLATE SPHEROIDAL SHAPE

2021 ◽  
Vol 9 (11) ◽  
pp. 683-690
Author(s):  
Rajeev Mishra ◽  
◽  
Sanjai Misra ◽  
Keyword(s):  
Fluid Dynamics ◽  
Boundary Conditions ◽  
Incompressible Fluid ◽  
Pressure Distribution ◽  
Oblate Spheroidal ◽  
Spheroidal Shape ◽  
Basic Equations ◽  
Spheroidal Coordinates

The paper studiesthe self-superposable motion of a liquid of a fluid which is incompressible in nature in oblate spheroidal shape. An incompressible fluid is defined as the fluid whose volume or density does not change with pressure. Thus, the main aim of this paper is to solve the basic equations of fluid dynamics in oblate spheroidal coordinates considering self-superposable nature of the fluid. The paper includes the study of nature of vorticity and irrotationality and has not considered the boundary conditions in theanalysis. Lastly, the paper determines the pressure distribution and the solutions contain a set of constants.

Energy conditions and modified gravity in anisotropic universe

2018 ◽  
Vol 96 (2) ◽  
pp. 225-232 ◽  
Author(s):  
H. Hossienkhani ◽  
V. Fayaz ◽  
A. Jafari
Keyword(s):  
Modified Gravity ◽  
General Scheme ◽  
Energy Condition ◽  
Momentum Tensor ◽  
Energy Conditions ◽  
Anisotropic Universe ◽  
Type I ◽  
De Sitter ◽  
Field Equations ◽  
New Formula

In this paper, energy conditions in a new [Formula: see text] modified gravity ([Formula: see text] and T represent the Gauss–Bonnet invariant and trace of the energy–momentum tensor, respectively) for anisotropic universe with perfect fluid are analyzed. In this model, we develop the general scheme for new [Formula: see text] modified gravity reconstruction from realistic anisotropic Bianchi type-I cosmology. Using de Sitter solution, the exact solutions of the field equations have been obtained. It is found that null and weak energy conditions are satisfied for the parameter range considered. As a result, the analyses show that the increase of anisotropy is attributed to the increase of weak energy condition.

scholarly journals A periodic varying deceleration parameter in f(R, T) gravity

2018 ◽  
Vol 33 (33) ◽  
pp. 1850193 ◽  
Author(s):  
P. K. Sahoo ◽  
S. K. Tripathy ◽  
Parbati Sahoo
Keyword(s):  
Deceleration Parameter ◽  
Momentum Conservation ◽  
Momentum Tensor ◽  
Oscillatory Behavior ◽  
Matter Content ◽  
Accelerated Expansion ◽  
Energy Conditions ◽  
Field Equations ◽  
Eos Parameter ◽  
Wide Range

The phenomenon of accelerated expansion of the present universe and a cosmic transit aspect is explored in the framework of a modified gravity theory known as f(R, T) gravity (where R is the Ricci scalar and T is the trace of the energy–momentum tensor of the matter content). The cosmic transit phenomenon signifies a signature flipping behavior of the deceleration parameter. We employ a periodic varying deceleration parameter and obtained the exact solution of field equations. The dynamical features of the model including the oscillatory behavior of the EOS parameter are studied. We have also explored the obvious violation of energy–momentum conservation in f(R, T) gravity. The periodic behavior of energy conditions for the model are also discussed with a wide range of the free parameters.

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