D‐dimensional torus as compact manifold and Kaluza–Klein cosmological model

1992 ◽  
Vol 33 (9) ◽  
pp. 3117-3127 ◽  
Author(s):  
S. K. Srivastava
Keyword(s):  
Cosmological Model ◽  
Compact Manifold ◽  
Dimensional Torus ◽  
Kaluza Klein

scholarly journals Kaluza–Klein Bulk Viscous Fluid Cosmological Models and the Validity of the Second Law of Thermodynamics in f(R, T) Gravity

2017 ◽  
Vol 72 (4) ◽  
pp. 365-374 ◽  
Author(s):  
Gauranga Charan Samanta ◽  
Ratbay Myrzakulov ◽  
Parth Shah
Keyword(s):  
Cosmological Model ◽  
Viscous Fluid ◽  
Second Law Of Thermodynamics ◽  
Second Law ◽  
Field Equations ◽  
Geometrical Properties ◽  
Bulk Viscous Fluid ◽  
Bulk Viscous ◽  
Two Stages ◽  
Kaluza Klein

Abstract:The authors considered the bulk viscous fluid in f(R, T) gravity within the framework of Kaluza–Klein space time. The bulk viscous coefficient (ξ) expressed as $\xi = {\xi _0} + {\xi _1}{{\dot a} \over a} + {\xi _2}{{\ddot a} \over {\dot a}},$ where ξ0, ξ1, and ξ2 are positive constants. We take p=(γ−1)ρ, where 0≤γ≤2 as an equation of state for perfect fluid. The exact solutions to the corresponding field equations are given by assuming a particular model of the form of f(R, T)=R+2f(T), where f(T)=λT, λ is constant. We studied the cosmological model in two stages, in first stage: we studied the model with no viscosity, and in second stage: we studied the model involve with viscosity. The cosmological model involve with viscosity is studied by five possible scenarios for bulk viscous fluid coefficient (ξ). The total bulk viscous coefficient seems to be negative, when the bulk viscous coefficient is proportional to ${\xi _2}{{\ddot a} \over {\dot a}},$ hence, the second law of thermodynamics is not valid; however, it is valid with the generalised second law of thermodynamics. The total bulk viscous coefficient seems to be positive, when the bulk viscous coefficient is proportional to $\xi = {\xi _1}{{\dot a} \over a},$$\xi = {\xi _1}{{\dot a} \over a} + {\xi _2}{{\ddot a} \over {\dot a}}$ and $\xi = {\xi _0} + {\xi _1}{{\dot a} \over a} + {\xi _2}{{\ddot a} \over {\dot a}},$ so the second law of thermodynamics and the generalised second law of thermodynamics is satisfied throughout the evolution. We calculate statefinder parameters of the model and observed that it is different from the ∧CDM model. Finally, some physical and geometrical properties of the models are discussed.

Kaluza-Klein Tilted Cosmological Model in Lyra Geometry

2017 ◽  
Vol 42 (3) ◽  
pp. 1451-1457 ◽  
Author(s):  
Subrata Kumar Sahu ◽  
Samuel Ganiamo Ganebo ◽  
Gebretsadik Gidey Weldemariam
Keyword(s):  
Cosmological Model ◽  
Lyra Geometry ◽  
Tilted Cosmological Model ◽  
Kaluza Klein

ROLE OF EXTRA DIMENSION IN ACCELERATED EXPANSION

2008 ◽  
Vol 23 (06) ◽  
pp. 909-917 ◽  
Author(s):  
K. D. PUROHIT ◽  
YOGESH BHATT
Keyword(s):  
Cosmological Model ◽  
Extra Dimension ◽  
Accelerated Expansion ◽  
Field Equations ◽  
Four Dimensions ◽  
Scale Factors ◽  
Expansion Of The Universe ◽  
The Universe ◽  
Kaluza Klein

A five-dimensional FRW-type Kaluza–Klein cosmological model is taken to study the role of extra dimension in the expansion of the universe. Relation between scale factors corresponding to conventional four dimensions and the extra dimension has been established. Field equations are solved in order to find out the effect of pressure corresponding to these scale factors. Conditions for accelerated expansion are derived.

scholarly journals Spherically symmetric T-solution of the equations of 5-dimensional Kaluza–Klein theory

2020 ◽  
Vol 28 (2) ◽  
pp. 51-56
Author(s):  
V. D. Gladush
Keyword(s):  
Cauchy Problem ◽  
Cosmological Model ◽  
Configuration Space ◽  
Jacobi Equation ◽  
Spherically Symmetric ◽  
Klein Theory ◽  
The Cauchy Problem ◽  
Hamilton Jacobi Equation ◽  
Hilbert Action ◽  
Kaluza Klein

A geometrodynamical approach to the five-dimensional (5D) spherically symmetric cosmological model in the Kaluza–Klein theory is constructed. After dimensional reduction, the 5D Hilbert action is reduced to the Einstein form describing the gravitational, electromagnetic, and scalar interacting fields. The subsequent transition to the configuration space leads to the supermetric and the Einstein–Hamilton–Jacobi equation, with the help of which the trajectories in the configuration space are found. Then the evolutionary coordinate is restored, and the Cauchy problem is solved to find the time dependence of the metric and fields. The configuration corresponds to a cosmological model of the Kantovsky–Sachs type, which has a hypercylinder topology and includes scalar and electromagnetic fields with contact interaction.

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