scholarly journals On weakly B symmetric pseudo Riemannian manifolds and its applications

Filomat ◽  
2021 ◽  
Vol 35 (3) ◽  
pp. 895-909
Author(s):  
Carlo Mantica ◽  
Uday De ◽  
Young Suh
Keyword(s):  
Equation Of State ◽  
Bulk Viscosity ◽  
Riemannian Manifolds ◽  
Geometric Properties ◽  
First Case ◽  
Imperfect Fluids

The object of the present paper is to study weakly B symmetric manifolds (WBS)n. At first some geometric properties of (WBS)n(n > 2) have been studied. Finally, we consider (WBS)4 spacetimes. They turn out to be both perfect and imperfect fluids Robertson-Walker space-times : an equation of state is provided in the first case, and in the second the nature of the bulk viscosity pressure is pointed out. Also, we construct an example of a (WBS)4.

scholarly journals A dynamical system analysis of f(R,T) gravity

2016 ◽  
Vol 13 (09) ◽  
pp. 1650108 ◽  
Author(s):  
Behrouz Mirza ◽  
Fatemeh Oboudiat
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Equation Of State ◽  
System Analysis ◽  
Equations Of Motion ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Future Singularity ◽  
First Case ◽  
Stress Energy

We investigate equations of motion and future singularities of [Formula: see text] gravity where [Formula: see text] is the Ricci scalar and [Formula: see text] is the trace of stress-energy tensor. Future singularities for two kinds of equation of state (barotropic perfect fluid and generalized form of equation of state) are studied. While no future singularity is found for the first case, some kind of singularity is found to be possible for the second. We also investigate [Formula: see text] gravity by the method of dynamical systems and obtain some fixed points. Finally, the effect of the Noether symmetry on [Formula: see text] is studied and the consistent form of [Formula: see text] function is found using the symmetry and the conserved charge.

Bulk viscosity in Friedmann universe with a varying speed of light described by modified equation of state

2015 ◽  
Vol 12 (10) ◽  
pp. 1550126
Author(s):  
G. S. Khadekar ◽  
Arti Ghogre
Keyword(s):  
Equation Of State ◽  
Bulk Viscosity ◽  
Scale Factor ◽  
Special Choice ◽  
Speed Of Light ◽  
Dependent Parameter ◽  
Expansion Of The Universe ◽  
The Universe ◽  
Modified Equation ◽  
Universe Evolution

We solve the Freidmann equations by considering a universe media as a bulk viscosity described by a modified equation of state (EOS) of the form p = (γ - 1)ρc2 + Λ(t). A completely integrable dynamical equation to the scale factor is obtained and gives out the exact solution by assuming that the time-dependent parameter Λ and the bulk viscosity are linear combination of two and three terms, respectively and is expressed as: [Formula: see text] and [Formula: see text], where R is a scale factor and Λ0, Λ1, ζ0, ζ1, ζ2, are constants. For a special choice of the parameters, we discuss the acceleration expansion of the universe evolution and future singularities in the framework of variable speed of light (VSL) theory.

VISCOUS GENERALIZED CHAPLYGIN GAS

2006 ◽  
Vol 15 (08) ◽  
pp. 1151-1161 ◽  
Author(s):  
XIANG-HUA ZHAI ◽  
YOU-DONG XU ◽  
XIN-ZHOU LI
Keyword(s):  
Equation Of State ◽  
Bulk Viscosity ◽  
Critical Energy ◽  
State Equation ◽  
Chaplygin Gas ◽  
Point Of View ◽  
Dynamical Analysis ◽  
Density Parameter ◽  
Generalized Chaplygin Gas ◽  
Barotropic Fluid

Viscous generalized Chaplygin gas (GCG) cosmology is discussed, assuming that there is bulk viscosity in the linear barotropic fluid and GCG. wγ = γ - 1 and wg represent the state equation parameters for barotropic fluid and GCG, respectively, in which γ = 1 or [Formula: see text] corresponds to ordinary matter or radiation. The dynamical analysis indicates that the phase [Formula: see text] is a dynamical attractor and the equation of state of GCG approaches it from either wg > -1 or wg < -1 depending on the choice of its initial cosmic density parameter and the ratio of pressure to critical energy density, where τg and τγ are viscosity parameters. Therefore, the equation of state wg will cross the boundary wg = -1 if we choose initial value wg < -1. Furthermore, we show that bulk viscosity coefficients should satisfy inequalities from the point of view of dynamics.

scholarly journals VISCOUS FRW COSMOLOGY IN MODIFIED GRAVITY

2005 ◽  
Vol 14 (11) ◽  
pp. 1899-1906 ◽  
Author(s):  
I. BREVIK ◽  
O. GORBUNOVA ◽  
Y. A. SHAIDO
Keyword(s):  
Equation Of State ◽  
Bulk Viscosity ◽  
Time Variation ◽  
Modified Gravity ◽  
Equations Of Motion ◽  
Frw Cosmology ◽  
Conservation Of Energy ◽  
Scalar Expansion ◽  
Big Rip ◽  
Energy And Momentum

We discuss a modified form of gravity implying that the action contains a power α of the scalar curvature. Coupling with the cosmic fluid is assumed. As equation of state for the fluid, we take the simplest version where the pressure is proportional to the density. Based upon a natural ansatz for the time variation of the scale factor, we show that the equations of motion are satisfied for a general α. Also the condition of conservation of energy and momentum is satisfied. Moreover, we investigate the case where the fluid is allowed to possess a bulk viscosity, and find the noteworthy fact that consistency of the formalism requires the bulk viscosity to be proportional to the power (2α-1) of the scalar expansion. In Einstein's gravity, where α = 1, this means that the bulk viscosity is proportional to the scalar expansion. This mathematical result is of physical interest; as discussed recently by the authors, there exists in principle a viscosity-driven transition of the fluid from the quintessence region into the phantom region, implying a future Big Rip singularity.

Inhomogeneous early viscous fluid universe: A concrete model for dark energy

2016 ◽  
Vol 13 (04) ◽  
pp. 1650037
Author(s):  
G. S. Khadekar
Keyword(s):  
Dark Energy ◽  
Equation Of State ◽  
Bulk Viscosity ◽  
Scale Factor ◽  
Inhomogeneous Equation ◽  
Special Choice ◽  
Field Equations ◽  
Dependent Parameter ◽  
Frw Model ◽  
The Universe

In this paper the dynamical equation of the scale factor of the universe is investigated to describe the effect of bulk viscosity on the early evolution of the universe. We assume the inhomogeneous equation of state of the form [Formula: see text], where the adiabatic parameter [Formula: see text] varies with the scale factor [Formula: see text] proposed by Carvalho [Unified description of early universe, Int. J. Theor. Phys. 35 (1996) 2019] and [Formula: see text] is a time-dependent parameter in the framework of the flat FRW model. From this modified equation of state the exact solution of the field equations is obtained by considering the bulk viscosity is a linear combination of two terms of the form: [Formula: see text] and cosmological constant [Formula: see text], where [Formula: see text] and [Formula: see text] are constants, in which an inflationary phase is followed by the radiation dominated phase. For a special choice of the parameter we can explain the dark energy dominant universe and Friedmann equations are solved for two different phases of the universe and obtain the [Formula: see text]–[Formula: see text] relation.

scholarly journals Bulk viscosity in F(T, TG) gravity

2017 ◽  
Vol 95 (3) ◽  
pp. 262-266
Author(s):  
M. Sharif ◽  
Kanwal Nazir
Keyword(s):  
Equation Of State ◽  
Bulk Viscosity ◽  
State Parameter ◽  
Time Dependent ◽  
Effective Equation ◽  
Phantom Divide ◽  
Equation Of State Parameter ◽  
Phantom Divide Line ◽  
Dependent Viscosity ◽  
The Universe

The present paper is devoted to exploring the effect of bulk viscosity in the context of F(T, TG) gravity. We consider a time-dependent viscosity model with a particular expression of Hubble parameter. We evaluate viscous effective equation of state parameter for three well-known F(T, TG) models. The behavior of the accelerated expanding universe is explored graphically through the viscous equation of state parameter. This parameter indicates the phantom-dominated era as well as crosses the phantom divide line for all three models. We conclude that the universe shows a transition from quintessence to phantom region in the presence of bulk viscosity.

Aspects of nonflat FRW bouncing models with quadratic equation of state

2018 ◽  
Vol 33 (35) ◽  
pp. 1850213 ◽  
Author(s):  
Ashutosh Singh ◽  
Rakesh Raushan ◽  
R. Chaubey ◽  
T. Singh
Keyword(s):  
General Relativity ◽  
Equation Of State ◽  
Bulk Viscosity ◽  
Second Law Of Thermodynamics ◽  
Quadratic Equation ◽  
Energy Conditions ◽  
Second Law ◽  
Generalized Second Law ◽  
Quadratic Equation Of State

In this paper, we investigate the possibility of a nonsingular model of universe in the framework of general relativity in nonflat FRW geometries with quadratic equation of state and bulk viscosity. We study whether a nonsingular bounce requires violation of energy conditions. We discuss the thermodynamical aspects of the resulting models with equilibrium description. In particular, we discuss the validity of the generalized second law of thermodynamics for resulting cosmologies.

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