scholarly journals Metric-Affine Version of Myrzakulov F(R,T,Q,?) Gravity and Cosmological Applications

Universe ◽  
2021 ◽  
Vol 7 (8) ◽  
pp. 262
Author(s):  
Damianos Iosifidis ◽  
Nurgissa Myrzakulov ◽  
Ratbay Myrzakulov
Keyword(s):  
Gravity Model ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Linear Case ◽  
Field Equations ◽  
Friedmann Equations ◽  
Complete Set

We derive the full set of field equations for the metric-affine version of the Myrzakulov gravity model and also extend this family of theories to a broader one. More specifically, we consider theories whose gravitational Lagrangian is given by F(R,T,Q,T,D) where T, Q are the torsion and non-metricity scalars, T is the trace of the energy-momentum tensor and D the divergence of the dilation current. We then consider the linear case of the aforementioned theory and, assuming a cosmological setup, we obtain the modified Friedmann equations. In addition, focusing on the vanishing non-metricity sector and considering matter coupled to torsion, we obtain the complete set of equations describing the cosmological behavior of this model along with solutions.

scholarly journals On the Splitting of the Einstein Field Equations with respect to General (1+3) Threading of Spacetime

2016 ◽  
Vol 2016 ◽  
pp. 1-15
Author(s):  
Aurel Bejancu ◽  
Hani Reda Farran
Keyword(s):  
Conservation Laws ◽  
Perfect Fluid ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Friedmann Equations ◽  
Flrw Universe

Based on general (1+3) threading of the spacetime (M,g), we obtain a new and simple splitting of both the Einstein field equations (EFE) and the conservation laws in (M,g). As an application, we obtain the splitting of EFE in an almost FLRW universe with energy-momentum tensor of a perfect fluid. In particular, we state the perturbation Friedmann equations in an almost FLRW universe.

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 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.

The wormhole thermodynamics in f (R ) gravity

2019 ◽  
Vol 35 (04) ◽  
pp. 1950360 ◽  
Author(s):  
A. S. Sefiedgar ◽  
M. Mirzazadeh
Keyword(s):  
Continuity Equation ◽  
Energy Momentum Tensor ◽  
Apparent Horizon ◽  
Second Law Of Thermodynamics ◽  
Momentum Tensor ◽  
Second Law ◽  
Standard Entropy ◽  
Field Equations ◽  
First Law Of Thermodynamics ◽  
Generalized Second Law

Thermodynamics of the evolving Lorentzian wormhole at the apparent horizon is investigated in [Formula: see text] gravity. Redefining the energy density and the pressure, the continuity equation is satisfied and the field equations in [Formula: see text] gravity reduce to the ones in general relativity. However, the energy–momentum tensor includes all the corrections from [Formula: see text] gravity. Therefore, one can apply the standard entropy-area relation within [Formula: see text] gravity. It is shown that there may be an equivalency between the field equations and the first law of thermodynamics. It seems that an equilibrium thermodynamics may be held on the apparent horizon. The validity of the generalized second law of thermodynamics (GSL) is also investigated in the wormholes.

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.

Various dark energy models for variables G and Λ in f(R, T) modified theory

2019 ◽  
Vol 34 (13) ◽  
pp. 1950098 ◽  
Author(s):  
Can Aktaş
Keyword(s):  
Dark Energy ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Tachyon Field ◽  
Field Equations ◽  
Frw Universe ◽  
Linearly Varying Deceleration Parameter ◽  
Energy Models ◽  
Modified Theory ◽  
Friedmann Robertson Walker

In this paper, we have researched tachyon field, k-essence and quintessence dark energy (DE) models for Friedmann–Robertson–Walker (FRW) universe with varying G and [Formula: see text] in f(R, T) gravitation theory. The theory of f(R, T) is proposed by Harko et al. [Phys. Rev. D 84, 024020, 2011]. In this theory, R is the Ricci scalar and T is the trace of energy–momentum tensor. For the solutions of field equations, we have used linearly varying deceleration parameter (LVDP), the equation of state (EoS) and the ratio between [Formula: see text] and Hubble parameter. Also, we have discussed some physical behavior of the models with various graphics.

Sign in / Sign up

Export Citation Format

Share Document