Kantowski-Sachs Universe Models in f(T)f(T) Theory of Gravity

The $f(T)$ theory is recently proposed to explain the present cosmic accelerating expansion of the universe. $f(T)$ theory is an extension of Teleparallel theory of gravity, where $T$ is the torsion scalar. This paper contains the construction of $f(T)$ models within the Kantowski-Sachs universe. For this purpose, we use conservation equation and equation of state parameter, which represents the different phases of the universe. We discuss possible cases for the matter dominated era, radiation dominated era, present dark energy phase and their combinations. Particularly, a constant solution has been obtained which may correspond to the cosmological constant. Further, we consider two well known $f(T)$ models and derive the equation of state parameter and discuss the cosmic acceleration. Also, the Hubble parameter and average scale factor have been evaluated.Comment: Accepted for publication in IJTP. arXiv admin note: substantial text overlap with arXiv:1105.6228 by other author

Teleparallel Energy-Momentum Distribution of Lewis-Papapetrou Spacetimes

In this paper, we find the energy-momentum distribution of stationary axisymmetric spacetimes in the context of teleparallel theory by using M$\ddot{o}$ller prescription. The metric under consideration is the generalization of the Weyl metrics called the Lewis-Papapetrou metric. The class of stationary axisymmetric solutions of the Einstein field equations has been studied by Galtsov to include the gravitational effect of an {\it external} source. Such spacetimes are also astrophysically important as they describe the exterior of a body in equilibrium. The energy density turns out to be non-vanishing and well-defined and the momentum becomes constant except along $\theta$-direction. It is interesting to mention that the results reduce to the already available results for the Weyl metrics when we take $\omega=0$.Comment: 13 pages, accepted for publication in Modern Physics Letters

Kinematic Self-Similar Solutions of Locally Rotationally Symmetric Spacetimes

This paper contains locally rotationally symmetric kinematic self-similar perfect fluid and dust solutions. We consider three families of metrics which admit kinematic self-similar vectors of the first, second, zeroth and infinite kinds, not only for the tilted fluid case but also for the parallel and orthogonal cases. It is found that the orthogonal case gives contradiction both in perfect fluid and dust cases for all the three metrics while the tilted case reduces to the parallel case in both perfect fluid and dust cases for the second metric. The remaining cases give self-similar solutions of different kinds. We obtain a total of seventeen independent solutions out of which two are vacuum. The third metric yields contradiction in all the cases.Comment: 17 pages, accepted for publication Brazilian J. Physic

Locally Rotationally Symmetric Vacuum Solutions in f(R) Gravity

This paper is devoted to find the Locally Rotationally Symmetric (LRS) vacuum solutions in the context of f(R) theory of gravity. Actually, we have considered the three metrics representing the whole family of LRS spacetimes and solved the field equations by using metric approach as well as the assumption of constant scalar curvature. It is mention here that R may be zero or non-zero. In all we found 10 different solutions.Comment: 22 pages, Accepted for publication in Int. J. Theor. Phy

Spatially Homogeneous Rotating Solution in f(R) Gravity and Its Energy Contents

In this paper, the metric approach of $f(R)$ theory of gravity is used to investigate the exact vacuum solutions of spatially homogeneous rotating spacetimes. For this purpose, R is replaced by f(R) in the standard Einstein-Hilbert action and the set of modified Einstein field equations reduce to a single equation. We adopt the assumption of constant Ricci scalar which maybe zero or non-zero. Moreover, the energy density of the non-trivial solution has been evaluated by using the generalized Landau-Lifshitz energy-momentum complex in the perspective of f(R) gravity for some appropriate f(R) model, which turns out to be a constant quantity.Comment: 10 page

A Study of Holographic Dark Energy Models in Chern-Simon Modified Gravity

This paper is devoted to study some holographic dark energy models in the context of Chern-Simon modified gravity by considering FRW universe. We analyze the equation of state parameter using Granda and Oliveros infrared cut-off proposal which describes the accelerated expansion of the universe under the restrictions on the parameter $\alpha$. It is shown that for the accelerated expansion phase $-1<\omega_{\Lambda}<-\frac{1}{3}$, the parameter $\alpha$ varies according as $1<\alpha<\frac{3}{2}$. Furthermore, for $0<\alpha<1$, the holographic energy and pressure density illustrates phantom-like theory of the evolution when $\omega_{\Lambda}<-1$. Also, we discuss the correspondence between the quintessence, K-essence, tachyon and dilaton field models and holographic dark energy models on similar fashion. To discuss the accelerated expansion of the universe, we explore the potential and the dynamics of quintessence, K-essence, tachyon and dilaton field models.Comment: 15 page

Ricci Dark Energy of Amended FRW Universe in Chern-Simon Modified Gravity

The energy density of the universe is proportional to the Ricci scalar curvature in the dynamical Chern-Simon (CS) modified gravity. In this paper, we consider the Amended Friedman-Robertson-Walker (AFRW) universe and explore its scale factor and the Ricci Dark Energy. THese turned out to be well-defined and definite. We compare the scale factors of FRW \cite{[17]}, Generalized Chaplygin gas (GCG) \cite{[18]} and AFRW models graphically. The combined graph of these models show that the behavior of both FRW and AFRW models is similar as these overlap each other for choosing particular values of the integration constants. Also, we draw a combined graph of the Ricci dark energy densities of FRW and AFRW models, in CS gravity, and the energy density of GCG. It shows that the densities of former two models are increasing with time while the energy density of GCG is decreasing.Comment: 11 pages,2 graphs. arXiv admin note: text overlap with arXiv:0909.1267 by other authors without attributio

Teleparallel Energy-Momentum Distribution of Locally Rotationally Symmetric Spacetimes

In this paper, we explore the energy-momentum distribution of locally rotationally symmetric (LRS) spacetimes in the context of the teleparallel theory of gravity by considering the three metrics, I, II and III, representing the whole class of LRS sapcetimes. In this regard, we use the teleparallel versions of the Einstein, Landau-Lifshitz, Bergmann-Thomson, and M$\ddot{o}$ller prescriptions. The results show that the momentum density components for the Einstein, Bergmann-Thomson, and M$\ddot{o}$ller prescriptions turn out to be same in all cases of the metrics I, II and III, but are different from those of the Landau- Lifshitz prescription, while the energy components remain the same for these three prescriptions only in all possible cases of the metrics I and II. We mention here that the M$\ddot{o}$ller energy-momentum distribution is independent of the coupling constant $\lambda$; that is, these results are valid for any teleparallel models.Comment: Accepted in Journal of Korean Physical Society. arXiv admin note: substantial text overlap with arXiv:0704.209

Exact solutions of Laplace equation by differential transform method

In this paper, we solve Laplace equation analytically by using differential transform method. For this purpose, we consider four models with two Dirichlet and two Neumann boundary conditions and obtain the corresponding exact solutions. The obtained results show the simplicity of the method and massive reduction in calculations when one compares it with other iterative methods, available in literature. It is worth mentioning that here only a few number of iterations are required to reach the closed form solutions as series expansions of some known functions.Comment: 8 pages, submitted for publicatio

Energy-Momentum Distribution of Non-Static Plane Symmetric Spacetimes in GR and TPT

This paper is devoted to explore the energy-momentum of non-static plane symmetric spacetimes in the context of General Relativity and teleparallel theory of gravity. For this purpose, we use four prescriptions, namely, Einstein, Landau-Lifshitz, Bergmann-Thomson and M{\o}ller in both theories. It is shown that the results for the first three prescriptions turn out to be same in both the theories but different for last prescription. It is mentioning here that our results coincide with the results obtained by Sharif and kanwal [1] for Bell-Szekeres metric under certain choice of the metric functions.Comment: 18 page