Spherically symmetric spacetime with radiating fluids in f(đť’˘, T) gravity

2019 â—˝  
Vol 34 (27) â—˝  
pp. 1950215 â—˝  
Author(s):  
M. Farasat Shamir â—˝  
Nabeeha Uzair
Keyword(s):  
Weyl Tensor â—˝  
Energy Momentum Tensor â—˝  
Stellar System â—˝  
Momentum Tensor â—˝  
Anisotropic Fluid â—˝  
Spherically Symmetric â—˝  
Field Equations â—˝  
Radiating Fluids â—˝  
Inhomogeneity Factor â—˝  
Symmetric Spacetime

The aim of this paper is to examine the irregularity factors of a self-gravitating stellar system in the existence of anisotropic fluid. We investigate the dynamics of field equations within [Formula: see text] background, where [Formula: see text] is the Gauss–Bonnet invariant and [Formula: see text] is the trace of the energy–momentum tensor. Moreover, we have investigated two differential equations using the conservation law and the Weyl tensor. We have determined the irregularity factors of spherical stellar system for some specific conditions of anisotropic and isotropic fluids, dust, radiating and non-radiating systems in [Formula: see text] gravity. It has been noted that the dissipative matter results in anisotropic stresses and makes the system more complex. The inhomogeneity factor is correlated to one of the scalar functions.

Spherically symmetric traversable wormholes in f(R2,T) gravity

2019 â—˝  
Vol 16 (10) â—˝  
pp. 1950147 â—˝  
Author(s):  
M. Zubair â—˝  
Quratulien Muneer â—˝  
Saira Waheed
Keyword(s):  
Modified Gravity â—˝  
Arbitrary Constant â—˝  
Energy Momentum Tensor â—˝  
Energy Condition â—˝  
Momentum Tensor â—˝  
Anisotropic Fluid â—˝  
Spherically Symmetric â—˝  
Matter Distribution â—˝  
Field Equations â—˝  
Traversable Wormholes

In this paper, we explore the possibility of wormhole solutions existence exhibiting spherical symmetry in an interesting modified gravity based on Ricci scalar term and trace of energy–momentum tensor. For this reason, we assume the matter distribution as anisotropic fluid and a specific viable form of the generic function given by [Formula: see text] involving [Formula: see text] and [Formula: see text], two arbitrary constant parameters. For having a simplified form of the resulting field equations, we assume three different forms of EoS of the assumed matter contents. In each case, we find the numerical wormhole solutions and analyze their properties for the wormhole existence graphically. The graphical behavior of the energy condition bounds is also investigated in each case. It is found that a realistic wormhole solutions satisfying all the properties can be obtained in each case.

Study of gravitational decoupled anisotropic solution

2019 â—˝  
Vol 28 (16) â—˝  
pp. 2040004
Author(s):  
M. Sharif â—˝  
Sobia Sadiq
Keyword(s):  
Energy Momentum Tensor â—˝  
Momentum Tensor â—˝  
Energy Conditions â—˝  
Spherically Symmetric â—˝  
Anisotropic Model â—˝  
Field Equations â—˝  
Anisotropic Solution â—˝  
Spherically Symmetric Solution â—˝  
Gravitational Source â—˝  
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 ON THE NATURAL GAUGE FIELDS OF MANIFOLDS

2000 â—˝  
Vol 15 (32) â—˝  
pp. 1991-2005 â—˝  
Author(s):  
A. B. PESTOV â—˝  
BIJAN SAHA
Keyword(s):  
Displacement Field â—˝  
Energy Momentum Tensor â—˝  
Linear Connection â—˝  
Momentum Tensor â—˝  
Gauge Fields â—˝  
Spherically Symmetric â—˝  
Time Inversion â—˝  
Field Equations â—˝  
Gauge Invariant â—˝  
Minkowski Space Time

The gauge symmetry inherent in the concept of manifold has been discussed. Within the scope of this symmetry the linear connection or displacement field can be considered as a natural gauge field on the manifold. The gauge-invariant equations for the displacement field have been derived. It has been shown that the energy–momentum tensor of this field conserves and hence the displacement field can be treated as one that transports energy and gravitates. To show the existence of the solutions of the field equations, we have derived the general form of the displacement field in Minkowski space–time which is invariant under rotation and space and time inversion. With this ansatz we found spherically-symmetric solutions of the equations in question.

scholarly journals PECULIAR ANISOTROPIC STATIONARY SPHERICALLY SYMMETRIC SOLUTION OF EINSTEIN EQUATIONS

2012 â—˝  
Vol 27 (09) â—˝  
pp. 1250044 â—˝  
Author(s):  
EMANUEL GALLO â—˝  
OSVALDO M. MORESCHI
Keyword(s):  
Dark Matter â—˝  
Energy Momentum Tensor â—˝  
Momentum Tensor â—˝  
Einstein Equations â—˝  
Spherically Symmetric â—˝  
Gravitational Lenses â—˝  
Field Equations â—˝  
Spherically Symmetric Solution â—˝  
Stress Energy â—˝  
Stress Energy Momentum Tensor

Motivated by studies on gravitational lenses, we present an exact solution of the field equations of general relativity, which is static and spherically symmetric, has no mass but has a nonvanishing spacelike components of the stress–energy–momentum tensor. In spite of its strange nature, this solution has nontrivial descriptions of gravitational effects. We show that the main aspects found in the dark matter phenomena can be satisfactorily described by this geometry. We comment on the relevance it could have to consider nonvanishing spacelike components of the stress–energy–momentum tensor ascribed to dark matter.

On a non-symmetric theory of the pure gravitational field

1958 â—˝  
Vol 54 (1) â—˝  
pp. 72-80 â—˝  
Author(s):  
D. W. Sciama
Keyword(s):  
Gravitational Field â—˝  
Energy Momentum Tensor â—˝  
Equations Of Motion â—˝  
Rest Mass â—˝  
Symmetric Tensor â—˝  
Momentum Tensor â—˝  
Unified Field Theory â—˝  
Field Equations â—˝  
Metric Tensor â—˝  
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 â—˝  
Author(s):  
Anirudh Pradhan â—˝  
Priyanka Garg â—˝  
Archana Dixit
Keyword(s):  
Energy Momentum Tensor â—˝  
Momentum Tensor â—˝  
Apparent Magnitude â—˝  
Physical Parameters â—˝  
Distance Modulus â—˝  
Luminosity Distance â—˝  
Field Equations â—˝  
Eos Parameter â—˝  
Accelerating Expansion â—˝  
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 â—˝  
Vol 30 (04) â—˝  
pp. 2150027
Author(s):  
I. Noureen â—˝  
Usman-ul-Haq â—˝  
S. A. Mardan
Keyword(s):  
Stability Analysis â—˝  
Energy Momentum Tensor â—˝  
Momentum Tensor â—˝  
Viscous Fluids â—˝  
Fluid Distribution â—˝  
Perturbation Scheme â—˝  
Field Equations â—˝  
Dynamical Equations â—˝  
Stability Of Stars â—˝  
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 â—˝  
Vol 14 (07) â—˝  
pp. 1233-1250 â—˝  
Author(s):  
M. FARHOUDI
Keyword(s):  
Energy Momentum Tensor â—˝  
Momentum Tensor â—˝  
Second Order â—˝  
Alternative Form â—˝  
Mathematical Form â—˝  
Einstein’S Field Equations â—˝  
Einstein’S Equations â—˝  
Field Equations â—˝  
Einstein's Equations â—˝  
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 Generalizing the coupling between geometry and matter: $$f\left( R,L_m,T\right) $$ gravity

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

scholarly journals The theory of spherically symmetric thin shells in conformal gravity

2018 â—˝  
Vol 27 (06) â—˝  
pp. 1841012 â—˝  
Author(s):  
Victor Berezin â—˝  
Vyacheslav Dokuchaev â—˝  
Yury Eroshenko
Keyword(s):  
General Relativity â—˝  
Weyl Tensor â—˝  
Delta Function â—˝  
Einstein Gravity â—˝  
Riemann Tensor â—˝  
Momentum Tensor â—˝  
Thin Shells â—˝  
Spherically Symmetric â—˝  
Gravitational Fields â—˝  
Gravitational Theories

The spherically symmetric thin shells are the nearest generalizations of the point-like particles. Moreover, they serve as the simple sources of the gravitational fields both in General Relativity and much more complex quadratic gravity theories. We are interested in the special and physically important case when all the quadratic in curvature tensor (Riemann tensor) and its contractions (Ricci tensor and scalar curvature) terms are present in the form of the square of Weyl tensor. By definition, the energy–momentum tensor of the thin shell is proportional to Diracs delta-function. We constructed the theory of the spherically symmetric thin shells for three types of gravitational theories with the shell: (1) General Relativity; (2) Pure conformal (Weyl) gravity where the gravitational part of the total Lagrangian is just the square of the Weyl tensor; (3) Weyl–Einstein gravity. The results are compared with these in General Relativity (Israel equations). We considered in detail the shells immersed in the vacuum. Some peculiar properties of such shells are found. In particular, for the traceless ([Formula: see text] massless) shell, it is shown that their dynamics cannot be derived from the matching conditions and, thus, is completely arbitrary. On the contrary, in the case of the Weyl–Einstein gravity, the trajectory of the same type of shell is completely restored even without knowledge of the outside solution.

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