Energy-Momentum Density of Non-Diagonal Bianchi Type Space-Time in General Relativity and Teleparallel Gravity

We calculated the energy-momentum density of non-diagonal Bianchi type space-time in two different theories of gravity, General relativity (GR) and the theory of Teleparallel gravity (TG). Firstly, by applying Einstein, Landau-Lifshitz, Bergmann-Thomson and Møller prescriptions, using double index complexes in GR. Secondly, in the frame work of TG, we used the energy momentum complexes of Einstein, Bergmann-Thomson and Landau-Lifshitz. We also study the spacial cases of non-diagonal Bianchi type space-time BII, BVIII and BIX. We obtained the same energy-momentum density components for Einstein and Bergmann-Thomson prescriptions for the above four mentioned space-times that we considered in our work. Also, we found that the energy density component in Møller prescription is zero for all Bianchi types space-times in GR. Furthermore, we show that if the metric components are functions of time t alone, then the total gravitational energy is identically zero.

Quintessence anisotropic stellar models in quadratic and Born-Infeld modified teleparallel Rastall gravity

This study aims to discuss anisotropic solutions that are spherically symmetric in the quintessence field,which describe compact stellar objects in the modified Rastall teleparallel theory of gravity.To achieve this goal,the Krori and Barua arrangement for spherically symmetric components of the line element is incorporated.We explore the field equations by selecting appropriate off-diagonal tetrad fields.Born-Infeld function of torsion f(T)=β√λT+1-1 and power law form h(T)=δTn are used.The Born-Infeld gravity was the first modified teleparallel gravity to discuss inflation.We use the linear equation of state pr=ξρto separate the quintessence density.After obtaining the field equations,we investigate different physical parameters that demonstrate the stability and physical acceptability of the stellar models.We use observational data,such as the mass and radius of the compact star candidates PSRJ 1416-2230,Cen X-3,&4U 1820-30,to ensure the physical plausibility of our findings.

General teleparallel gravity from Finsler geometry

Riemannian geometry, as a basis for general relativity, can be obtained from the more general Finsler geometry in terms of the Cartan connection and Chern connection, as discussed frequently in the literature. However, there are other gravity theories that can be made to be equivalent to general relativity but are based on non-Riemannian geometry. Famous examples are the Teleparallel and Symmetric Teleparallel gravity theories. In this paper, we show how to obtain the geometry for Teleparallel gravity from Finsler geometry in terms of a ‘Teleparallel type’ connection.

Generic phase portrait analysis of finite-time singularities and generalized Teleparallel gravity

We analyze the four common types of finite-time singularity using a generic framework of the phase portrait geometric approach. This technique requires the Friedmann system to be written as a one-dimensional autonomous system. We employ a scale factor that has been used widely in the literature to realize the four finite- time singularity types, then we give a detailed discussion for each case showing possible novel models. Moreover, we show how different singularity types can play essential roles in different cosmological scenarios. Among several modified gravity theories, we show that the f（T） cosmology is compatible with the phase portrait analysis, since the field equations include Hubble derivatives only up to first order. Therefore, we reconstruct the f（T） theory which generates these phase portraits. We also perform a complementary analysis using the effective equation of state. Furthermore, we investigate the role of the torsion fluid in realizing the cosmic singularities.

Interpretation of Rotation Curves of Spiral Galaxies in Modified Teleparallel Gravity

There is a significant difference between the calculation based on the theory of general relativity and observation of rotation curves of spiral galaxies. To describe this discrepancy, two distinct theories have been proposed so far： existence of dark matter and modification of underlying gravitational theory. In the absence of dark matter, it is assumed that the theory of general relativity on galactic scales needs to be modified. This letter is devoted to explaining this difference in a modified teleparMIeI gravity. We show that modified teleparallel gravity favors flatness of rotation curves of spiral galaxies much in the same way as observation shows.

Teleparallel equivalent theory of (1+1)-dimensional gravity

A theory of （1＋1）-dimensional gravity is constructed on the basis of the teleparallel equivalent of general relativity. The fundamental field variables are the tetrad fields ei^μ and the gravity is attributed to the torsion. A dilatonic spherically symmetric exact solution of the gravitational field equations characterized by two parameters M and Q is derived. The energy associated with this solution is calculated using the two-dimensional gravitational energy- momentum formula.

Energy and momentum of general spherically symmetric frames on the regularizing teleparallelism

In the context of the covariant teleparallel framework, we use the 2-form translational momentum to compute the total energy of two general spherically symmetric frames. The first one is characterized by an arbitrary function H（r）, which preserves the spherical symmetry and reproduces all the previous solutions, while the other one is characterized by a parameter ξ which ensures the vanishing of the axial of trace of the torsion. We calculate the total energy by using two procedures, i.e., when the WeitzenbSck connection Гα^β is trivial, and show how H（r） and ξ play the role of an inertia that leads the total energy to be unphysical. Therefore, we take into account Гα^β and show that although the spacetimes we use contain an arbitrary function and one parameter, they have no effect on the form of the total energy and momentum as it should be.

Energy and spatial momentum of charged rotating frames in tetrad gravity

We compute the total energy and the spatial momentum of four charged rotating （Kerr-Newman） frames by using the gravitational energy-momentum 3-form within the framework of the tetrad formulation of the general relativity theory. We show how the effect of the inertial always makes the total energy divergent. We use a natural regularization method, which yields the physical value for the total energy of the system. We show how the regularization method works on a number of different rotating frames that are related to each other by the local Lorentz transformation. We also show that the inertial has no effect on the spatial momentum components.

Energy and momentum of rotating frames in tetrad gravity

Within the framework of the tetrad formulation of general relativity theory, we compute the total energy and momentum of four rotating frames using the gravitational energy-momentum 3-form. We show how the effect of inertia always makes the total energy divergent. We use a natural regularization method to obtain physical values for the total energy of the system and show how it works on a number of explicit examples. We also show by calculation that inertia has no effect on the momentum components.

On the Energy-Momentum Problem in Static Einstein Universe

The energy-momentum distributions of Einstein＇s simplest static geometrical model for an isotropic and homogeneous universe are evaluated. For this purpose, Einstein, Bergmann-Thomson, Landau-Lifshitz （LL）, Moller and Papapetrou energy-momentum complexes are used in general relativity. While Einstein and Bergmann-Thomson complexes give exactly the same results, LL and Papapetrou energy-momentum complexes do not provide the same energy densities. The Moller energy-momentum density is found to be zero everywhere in Einstein＇s universe. Also, several spacetimes are the limiting cases considered here.

Reconstructing f(T) modified gravity from ECHDE and ECNADE models

We investigate alternative candidates to dark energy(DE) that can explain the current state of the Universe in the framework of the generalized teleparallel theory of gravity f(T), where T denotes the torsion scalar. To achieve this, we carry out a series of reconstructions taking into account the ordinary and entropy-corrected versions of the holographic and new agegraphic DE models.These models are used as alternatives to DE in the literature in order to describe the current state of our Universe. It is remarked that the proposed models indicate behavior akin to phantom or quintessence models. Furthermore, we also generate the parameters of the equation of state associated with entropy-corrected models and we observe a phase transition between the quintessence state and phantom state as it is shown by the recent observational data. We also investigate the stability of these models and we create the {r-s} trajectories and compare with the ΛCDM limit. The behavior of certain physical parameters such as the speed of sound and the Statefinder diagnostic pair {r-s} is compatible with the current observational data.

Gravitational leptogenesis in teleparallel and symmetric teleparallel gravities

In this study,we investigate the possibilities of generating baryon number asymmetry under thermal equilibrium within the frameworks of teleparallel and symmetric teleparallel gravities.Through the derivative couplings of the torsion scalar and the non-metricity scalar to baryons,baryon number asymmetry is produced in the radiation dominated epoch.For gravitational baryogenesis mechanisms in these two frameworks,the produced baryon-to-entropy ratio is too small to be consistent with observations.However,the gravitational leptogenesis models within both frameworks have the potential to explain the observed baryon-antibaryon asymmetry.