scholarly journals Models of Collapsing and Expanding Cylindrical Source in f(R,T) Theory

2019 ◽  
Vol 2019 ◽  
pp. 1-16
Author(s):  
M. Sharif ◽  
Aisha Siddiqa
Keyword(s):  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Maxwell Field ◽  
Energy Conditions ◽  
Field Equations ◽  
Anisotropic Parameter ◽  
Model Parameter ◽  
Expansion Scalar ◽  
Cylindrical Source ◽  
Charged Cylinder

We discuss the collapsing and expanding solutions of anisotropic charged cylinder in the context of f(R,T) theory (R represents the Ricci scalar and T denotes the trace of energy-momentum tensor). For this purpose, we take an auxiliary solution of Einstein-Maxwell field equations and evaluate expansion scalar whose negative values lead to collapse and positive values give expansion. For both cases, the behavior of density, pressure, anisotropic parameter, and mass is explored and the effects of charge as well as model parameter on these quantities are examined. The energy conditions are found to be satisfied for both solutions.

Models of charged self-gravitating source in f(R,T) theory

2018 ◽  
Vol 27 (16) ◽  
pp. 1950005 ◽  
Author(s):  
M. Sharif ◽  
Aisha Siddiqa
Keyword(s):  
Momentum Tensor ◽  
Energy Conditions ◽  
Radial Coordinate ◽  
Physical Parameters ◽  
Field Equations ◽  
Expansion Formula ◽  
Anisotropic Parameter ◽  
Spherical Source ◽  
Model Parameter ◽  
Theory Formula

We discuss the anisotropic nonstatic charged spherical source describing the phenomena of collapse and expansion in the context of [Formula: see text] theory ([Formula: see text] is the Ricci scalar and [Formula: see text] is the trace of energy–momentum tensor). The Einstein–Maxwell field equations are formulated and an auxiliary solution is considered. We evaluate the corresponding expansion scalar [Formula: see text] and investigate the cases of collapse [Formula: see text] and expansion ([Formula: see text]). In both cases, we explore the influence of charge as well as model parameter on density, radial/tangential pressure, anisotropic parameter and mass through graphs. It is observed that the physical parameters vary with time for expansion while remain constant for collapse. However, the change with respect to the radial coordinate is the same for both cases. The model parameter has the same impact in both cases while charge affects only in the case of collapse. The energy conditions are satisfied for both solutions with particular values of the parameters.

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.

scholarly journals STRING COSMOLOGY IN ANISOTROPIC BIANCHI-II SPACETIME

2011 ◽  
Vol 26 (11) ◽  
pp. 779-793 ◽  
Author(s):  
SURESH KUMAR
Keyword(s):  
Cosmological Model ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Hubble’S Parameter ◽  
Massive String ◽  
Field Equations ◽  
Expansion Scalar ◽  
Spatially Homogeneous ◽  
The Universe ◽  
Shear Tensor

The present study deals with a spatially homogeneous and anisotropic Bianchi-II cosmological model representing massive strings. The energy–momentum tensor, as formulated by Letelier,10 has been used to construct a massive string cosmological model for which the expansion scalar is proportional to one of the components of shear tensor. The Einstein's field equations have been solved by applying a variation law for generalized Hubble's parameter that yields a constant value of deceleration parameter in Bianchi-II spacetime. A comparative study of accelerating and decelerating modes of the evolution of universe has been carried out in the presence of string scenario. The study reveals that massive strings dominate the early Universe. The strings eventually disappear from the Universe for sufficiently large times, which is in agreement with the current astronomical observations.

scholarly journals Compact star in Tolman–Kuchowicz spacetime in the background of Einstein–Gauss–Bonnet gravity

2019 ◽  
Vol 79 (11) ◽  
Author(s):  
Piyali Bhar ◽  
Ksh. Newton Singh ◽  
Francisco Tello-Ortiz
Keyword(s):  
General Relativity ◽  
Energy Momentum Tensor ◽  
Compact Star ◽  
Momentum Tensor ◽  
Energy Conditions ◽  
Coupling Constant ◽  
Field Equations ◽  
Bonnet Gravity ◽  
Principal Directions ◽  
Hilbert Action

Abstract The present work is devoted to the study of anisotropic compact matter distributions within the framework of five-dimensional Einstein–Gauss–Bonnet gravity. To solve the field equations, we have considered that the inner geometry is described by Tolman–Kuchowicz spacetime. The Gauss–Bonnet Lagrangian $$\mathcal {L}_{GB}$$LGB is coupled to the Einstein–Hilbert action through a coupling constant, namely $$\alpha $$α. When this coupling tends to zero general relativity results are recovered. We analyze the effect of this parameter on the principal salient features of the model, such as energy density, radial and tangential pressure and anisotropy factor. These effects are contrasted with the corresponding general relativity results. Besides, we have checked the incidence on an important mechanism: equilibrium by means of a generalized Tolman–Oppenheimer–Volkoff equation and stability through relativistic adiabatic index and Abreu’s criterion. Additionally, the behavior of the subliminal sound speeds of the pressure waves in the principal directions of the configuration and the conduct of the energy-momentum tensor throughout the star are analyzed employing the causality condition and energy conditions, respectively. All these subjects are illuminated by means of physical, mathematical and graphical surveys. The M–I and the M–R graphs imply that the stiffness of the equation of state increases with $$\alpha $$α; however, it is less stiff than GR.

On a non-symmetric theory of the pure gravitational field

1958 ◽  
Vol 54 (1) ◽  
pp. 72-80 ◽  
Author(s):  
D. W. Sciama
Keyword(s):  
Gravitational Field ◽  
Energy Momentum Tensor ◽  
Equations Of Motion ◽  
Rest Mass ◽  
Symmetric Tensor ◽  
Momentum Tensor ◽  
Unified Field Theory ◽  
Field Equations ◽  
Metric Tensor ◽  
Unified Field

ABSTRACTIt is suggested, on heuristic grounds, that the energy-momentum tensor of a material field with non-zero spin and non-zero rest-mass should be non-symmetric. The usual relationship between energy-momentum tensor and gravitational potential then implies that the latter should also be a non-symmetric tensor. This suggestion has nothing to do with unified field theory; it is concerned with the pure gravitational field.A theory of gravitation based on a non-symmetric potential is developed. Field equations are derived, and a study is made of Rosenfeld identities, Bianchi identities, angular momentum and the equations of motion of test particles. These latter equations represent the geodesics of a Riemannian space whose contravariant metric tensor is gij–, in agreement with a result of Lichnerowicz(9) on the bicharacteristics of the Einstein–Schrödinger field equations.

FRW cosmological models with cosmological constant in f (R,T) theory of gravity

2021 ◽  
Author(s):  
Anirudh Pradhan ◽  
Priyanka Garg ◽  
Archana Dixit
Keyword(s):  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Apparent Magnitude ◽  
Physical Parameters ◽  
Distance Modulus ◽  
Luminosity Distance ◽  
Field Equations ◽  
Eos Parameter ◽  
Accelerating Expansion ◽  
Frw Cosmological Model

In the present paper, we have generalized the behaviors of {\color{blue}transit-decelerating to accelerating} FRW cosmological model in f (R, T) gravity theory, where R, T are Ricci scalar and trace of energy-momentum tensor respectively. The solution of the corresponding field equations is obtained by assuming a linear function of the Hubble parameter H, i.e., q = c<sub>1</sub> + c<sub>2</sub>H which gives a time-dependent DP (deceleration parameter) q(t)=-1+\frac{c_2}{\sqrt{2c_2 t +c_3}}, where c<sub>3</sub> and c<sub>2</sub> are arbitrary integrating constants [Tiwari et al., Eur. Phys. J. Plus: 131, 447 (2016); 132, 126 (2017)]. There are two scenarios in which we explain the particular form of scale factor thus obtained  (i) By using the recent constraints from OHD and JLA data which shows a cosmic deceleration to acceleration and (ii) By using new constraints from supernovae type la union data which shows accelerating expansion universe (q<0) throughout the evolution. We have observed that the EoS parameter, energy density parameters, and important cosmological planes yield the results compatible with the modern observational data. For the derived models, we have calculated various physical parameters as Luminosity distance, Distance modulus, and Apparent magnitude versus redshift for both supporting current observations.

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 CLASSICAL TRACE ANOMALY

2005 ◽  
Vol 14 (07) ◽  
pp. 1233-1250 ◽  
Author(s):  
M. FARHOUDI
Keyword(s):  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Second Order ◽  
Alternative Form ◽  
Mathematical Form ◽  
Einstein’S Field Equations ◽  
Einstein’S Equations ◽  
Field Equations ◽  
Einstein's Equations ◽  
Trace Anomaly

We seek an analogy of the mathematical form of the alternative form of Einstein's field equations for Lovelock's field equations. We find that the price for this analogy is to accept the existence of the trace anomaly of the energy–momentum tensor even in classical treatments. As an example, we take this analogy to any generic second order Lagrangian and exactly derive the trace anomaly relation suggested by Duff. This indicates that an intrinsic reason for the existence of such a relation should perhaps be, classically, somehow related to the covariance of the form of Einstein's equations.

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.

scholarly journals Generalizing the coupling between geometry and matter: $$f\left( R,L_m,T\right) $$ gravity

2021 ◽  
Vol 81 (7) ◽  
Author(s):  
Zahra Haghani ◽  
Tiberiu Harko
Keyword(s):  
Gravitational Field ◽  
Energy Momentum Tensor ◽  
Equations Of Motion ◽  
Momentum Tensor ◽  
Newtonian Limit ◽  
Gravity Models ◽  
Momentum Balance ◽  
Field Equations ◽  
Gravitational Fields ◽  
Generalized Poisson

AbstractWe generalize and unify the $$f\left( R,T\right) $$ f R , T and $$f\left( R,L_m\right) $$ f R , L m type gravity models by assuming that the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar R, of the trace of the energy–momentum tensor T, and of the matter Lagrangian $$L_m$$ L m , so that $$ L_{grav}=f\left( R,L_m,T\right) $$ L grav = f R , L m , T . We obtain the gravitational field equations in the metric formalism, the equations of motion for test particles, and the energy and momentum balance equations, which follow from the covariant divergence of the energy–momentum tensor. Generally, the motion is non-geodesic, and takes place in the presence of an extra force orthogonal to the four-velocity. The Newtonian limit of the equations of motion is also investigated, and the expression of the extra acceleration is obtained for small velocities and weak gravitational fields. The generalized Poisson equation is also obtained in the Newtonian limit, and the Dolgov–Kawasaki instability is also investigated. The cosmological implications of the theory are investigated for a homogeneous, isotropic and flat Universe for two particular choices of the Lagrangian density $$f\left( R,L_m,T\right) $$ f R , L m , T of the gravitational field, with a multiplicative and additive algebraic structure in the matter couplings, respectively, and for two choices of the matter Lagrangian, by using both analytical and numerical methods.

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