A Kerr Metric Solution in Tetrad Theory of Gravitation

Using an axial parallel vector field we obtain two exact solutions of a vacuum gravitational field equations. One of the exact solutions gives the Schwarzschild metric while the other gives the Kerr metric. The parallel vector field of the Kerr solution have an axial symmetry. The exact solution of the Kerr metric contains two constants of integration, one being the gravitational mass of the source and the other constant $h$ is related to the angular momentum of the rotating source, when the spin density ${S_{i j}}^\mu$ of the gravitational source satisfies $\partial_\mu {S_{i j}}^\mu=0$. The singularity of the Kerr solution is studied

Isotropic stars in higher-order torsion scalar theories

Two tetrad spaces reproducing spherically symmetric spacetime are applied to the equations of motion of higher-order torsion theories. Assuming the existence of conformal Killing vector, two isotropic solutions are derived. We show that the first solution is not stable while the second one confirms a stable behavior. We also discuss the construction of the stellar model and show that one of our solution capable of such construction while the other cannot. Finally, we discuss the generalized Tolman-Oppenheimer-Volkoff and show that one of our models has a tendency to equilibrium.Comment: 16 pages Latex, 5 figures, will appear in Adv. High Energy Phys. (2016

Wormhole solution and Energy in Teleparallel Theory of Gravity

An exact solution is obtained in the tetrad theory of gravitation. This solution is characterized by two-parameters $k_1, k_2$ of spherically symmetric static Lorentzian wormhole which is obtained as a solution of the equation $\rho=\rho_t=0$ with $\rho=T_{i,j}u^iu^j$, $\rho_t=(T_{ij}-\displaystyle{1 \over 2}Tg_{ij}) u^iu^j$ where $u^iu_i=-1$. From this solution which contains an arbitrary function we can generates the other two solutions obtained before. The associated metric of this spacetime is a static Lorentzian wormhole and it includes the Schwarzschild black hole, a family of naked singularity and a disjoint family of Lorentzian wormholes. Calculate the energy content of this tetrad field using the gravitational energy-momentum given by M{\o}ller in teleparallel spacetime we find that the resulting form depends on the arbitrary function and does not depend on the two parameters $k_1$ and $k_2$ characterize the wormhole. Using the regularized expression of the gravitational energy-momentum we get the value of energy does not depend on the arbitrary function.Comment: 11 pages Late