scholarly journals MØLLER ENERGY–MOMENTUM PRESCRIPTION FOR A LOCALLY ROTATIONALLY SYMMETRIC SPACE–TIME

2006 ◽  
Vol 21 (18) ◽  
pp. 3845-3853 ◽  
Author(s):  
OKTAY AYDOGDU
Keyword(s):  
General Relativity ◽  
Energy Distribution ◽  
Bianchi Type ◽  
Space Time ◽  
Type Ii ◽  
Theory Of Relativity ◽  
Locally Rotationally Symmetric ◽  
Rotationally Symmetric ◽  
Teleparallel Theory ◽  
The Universe

The energy distribution in the Locally Rotationally Symmetric (LRS) Bianchi type II space–time is obtained by considering the Møller energy–momentum definition in both Einstein's theory of general relativity and teleparallel theory of relativity. The energy distribution which includes both the matter and gravitational field is found to be zero in both of these different gravitation theories. This result agrees with previous works of Cooperstock and Israelit, Rosen, Johri et al., Banerjee and Sen, Vargas, and Aydogdu and Salti. Our result — the total energy of the universe is zero — supports the view points of Albrow and Tryon.

scholarly journals GRAVITATIONAL ENERGY–MOMENTUM DENSITY IN BIANCHI TYPE II SPACE–TIMES

2006 ◽  
Vol 15 (04) ◽  
pp. 459-468 ◽  
Author(s):  
OKTAY AYDOGDU
Keyword(s):  
General Relativity ◽  
Energy Distribution ◽  
Total Energy ◽  
Bianchi Type ◽  
Teleparallel Gravity ◽  
Momentum Density ◽  
Gravitational Energy ◽  
Type Ii ◽  
Rotationally Symmetric ◽  
Total Energy Distribution

In this paper, using Einstein, Landau and Lifshitz's energy–momentum complexes both in general relativity and teleparallel gravity, we calculate the total energy distribution (due to matter and fields, including gravitation) associated with locally rotationally symmetric (LRS) Bianchi type II cosmological models. We show that energy densities in these different gravitation theories are the same, so they agree with each other. We obtain the result that the total energy is zero. This result agrees with previous works of Cooperstock and Israelit, Rosen, Johri et al., Banerjee and Sen, Vargas, Aydogdu and Saltı. Moreover, our result supports the viewpoints of Albrow and Tryon.

Locally rotationally symmetric (LRS) Bianchi type II string dust viscous fluid cosmological models in Lyra geometry

2014 ◽  
Vol 92 (12) ◽  
pp. 1714-1719 ◽  
Author(s):  
Raj Bali ◽  
Mahesh Kumar Yadav ◽  
Lokesh Kumar Gupta
Keyword(s):  
Cosmological Model ◽  
Viscous Fluid ◽  
Bulk Viscosity ◽  
Bianchi Type ◽  
Displacement Vector ◽  
Lyra Geometry ◽  
Type Ii ◽  
Locally Rotationally Symmetric ◽  
Rotationally Symmetric ◽  
The Universe

In the present study, a locally rotationally symmetric Bianchi type II string dust cosmological model with varying bulk viscosity in the framework of Lyra geometry is investigated. To get the deterministic solution, we have assumed that shear (σ) is proportional to the expansion (θ) and ζθ = constant, where ζ is the coefficient of bulk viscosity. The ansatz ζθ = constant, was found to coincide with the occurrence of Little Rip (LR) cosmology using Friedmann–Robertson–Walker metric (Breviket al. Phys. Rev. D, 84, 103508-1-6 (2011)). The model describes the pre-inflationary stage of the universe. The presence of viscosity leads to inflationary-like solutions. Anisotropy is maintained because of the presence of strings. The presence of bulk viscosity prevents the matter density from vanishing. In a special case, the model represents the isotropy of the universe. The universe passes through a decelerating stage to an accelerating phase, which is in agreement with Ries et al.’s (Astrophys. J. 607, 665 (2004). doi:10.1086/383612 ) type Ia supernovae astronomical observations. The displacement vector (β) of Lyra geometry is a decreasing function of time analogous to the cosmological constant (Λ) of general relativity. We have attempted to explore the possibility of constructing a string dust viscous fluid cosmological model in Bianchi type II space–time with displacement vector (β) in Lyra geometry using the geometric condition that shear is proportional to expansion.

scholarly journals Nonlinear Spinor Field in Non-Diagonal Bianchi Type Space-Time

2018 ◽  
Vol 173 ◽  
pp. 02018
Author(s):  
Bijan Saha
Keyword(s):  
Spinor Field ◽  
Bianchi Type ◽  
Space Time ◽  
Coupling Constant ◽  
Nonlinear Spinor ◽  
Bianchi Models ◽  
Rotationally Symmetric ◽  
Big Crunch ◽  
The Universe

Within the scope of the non-diagonal Bianchi cosmological models we have studied the role of the spinor field in the evolution of the Universe. In the non-diagonal Bianchi models the spinor field distribution along the main axis is anisotropic and does not vanish in the absence of the spinor field nonlinearity. Hence within these models perfect fluid, dark energy etc. cannot be simulated by the spinor field nonlinearity. The equation for volume scale V in the case of non-diagonal Bianchi models contains a term with first derivative of V explicitly and does not allow exact solution by quadratures. Like the diagonal models the non-diagonal Bianchi space-time becomes locally rotationally symmetric even in the presence of a spinor field. It was found that depending on the sign of the coupling constant the model allows either an open Universe that rapidly grows up or a close Universe that ends in a Big Crunch singularity.

A NOTE ON KILLING VECTOR FIELDS OF BIANCHI TYPE II SPACETIMES IN TELEPARALLEL THEORY OF GRAVITATION

2010 ◽  
Vol 25 (20) ◽  
pp. 1733-1740 ◽  
Author(s):  
GHULAM SHABBIR ◽  
SUHAIL KHAN
Keyword(s):  
General Relativity ◽  
Vector Fields ◽  
Bianchi Type ◽  
Killing Vector ◽  
Type Ii ◽  
Direct Integration ◽  
Integration Technique ◽  
Killing Vector Fields ◽  
Teleparallel Theory ◽  
Theory Of Gravitation

The aim of this paper is to classify Bianchi type II spacetimes according to their teleparallel Killing vector fields using the direct integration technique. Studying teleparallel Killing vector fields in the above spacetimes, it turns out that the dimensions of the teleparallel Killing vector fields are 4, 5 or 7. A brief comparison between teleparallel and general relativity Killing vector fields are given. It is shown that for the above spacetimes in the presence of torsion we get more conservation laws which are different from the theory of general relativity.

scholarly journals Mixed fluid cosmological model in f(R, T) gravity

2020 ◽  
Vol 98 (11) ◽  
pp. 1015-1022 ◽  
Author(s):  
Parbati Sahoo ◽  
Barkha Taori ◽  
K.L. Mahanta
Keyword(s):  
Cosmological Model ◽  
Bianchi Type ◽  
Type I ◽  
Time Varying ◽  
Eos Parameter ◽  
Barotropic Fluid ◽  
Rotationally Symmetric ◽  
Expansion Of The Universe ◽  
The Universe ◽  
Mixed Fluid

We construct a locally rotationally symmetric (LRS) Bianchi type-I cosmological model in f(R, T) theory of gravity when the source of gravitation is a mixture of barotropic fluid and dark energy (DE) by employing a time-varying deceleration parameter. We observe through the behavior of the state finder parameters (r, s) that our model begins from the Einstein static era and goes to ΛCDM era. The equation of state (EOS) parameter (ωd) for DE varies from the phantom (ω < –1) phase to quintessence (ω > –1) phase, which is consistent with observational results. It is found that the discussed model can reproduce the current accelerating phase of the expansion of the universe.

Sign in / Sign up

Export Citation Format

Share Document