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Regularization of f(T) Gravity Theories and Local Lorentz Transformation
Get PDFWe regularized the field equations of f(T) gravity theories such that the effect of local Lorentz transformation (LLT), in the case of spherical symmetry, is removed. A “general tetrad field,” with an arbitrary function of radial coordinate preserving spherical symmetry, is provided. We split that tetrad field into two matrices; the first represents a LLT, which contains an arbitrary function, and the second matrix represents a proper tetrad field which is a solution to the field equations of f(T) gravitational theory (which are not invariant under LLT). This “general tetrad field” is then applied to the regularized field equations of f(T). We show that the effect of the arbitrary function which is involved in the LLT invariably disappears
Axially Symmetric-dS Solution in Teleparallel f(T) Gravity Theories
Get PDFWe apply a tetrad field with six unknown functions to Einstein field equations. Exact vacuum solution, which represents axially symmetric-dS spacetime, is derived. We multiply the tetrad field of the derived solution by a local Lorentz transformation which involves a generalization of the angle ϕ and get a new tetrad field. Using this tetrad, we get a differential equation from the scalar torsion T=TαμνSαμν. Solving this differential equation we obtain a solution to the f(T) gravity theories under certain conditions on the form of f(T) and its first derivatives. Finally, we calculate the scalars of Riemann Christoffel tensor, Ricci tensor, Ricci scalar, torsion tensor, and its contraction to explain the singularities associated with this solution
Schwarzschild solution in extended teleparallel gravity
No full textA tetrad field with two unknown functions of the radial coordinate and an angle Φ (the polar angle ϕ times a function of the radial coordinate), is applied to the field equation of the modified theory of gravity. An exact vacuum solution is derived; its scalar torsion, , is constant. When the angle Φ coincides with the polar angle ϕ, the derived solution will be a solution only for the linear form of the f(T) gravitational theory
Isotropic Stars in Higher-Order Torsion Scalar Theories
Get PDFTwo different nondiagonal tetrad spaces reproducing spherically symmetric spacetime are applied to the field equations of higher-order torsion scalar 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 solutions is capable of such construction while the other is not. Finally, we discuss the generalized Tolman-Oppenheimer-Volkoff and show that one of our models has a tendency to equilibrium
Gravitational energy, momentum and angular momentum of Schwarzschild Anti-de Sitter space-times in the teleparallel equivalent of general relativity
No full textSpherically Symmetric Geometries in f(T) and f(R) Gravitational Theories
Get PDFUsing the well know relation between Ricci scalar, R, and torsion scalar, T, that is, R=-T-2∇αTα, we show that, for any spherically symmetric spacetime whose (i) scalar torsion vanishing, that is, T=TμναSαμν=0 or (ii) total derivative term, that is, ∇αTα with Tα is the contraction of the torsion, vanishing, or (iii) the combination of scalar torsion and total derivative term vanishing, could be solution for f(T) and f(R) gravitational theories
Killing vectors of Schwarzschild space-times in teleparallel equivalent of general relativity
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Momentum in Teleparallel Equivalent of General Relativity
No full textA new exact solution describing a general stationary and axisymmetric object of the gravitational field in the framework of teleparallel equivalent of general relativity TEGR is derived. The solution is characterized by three parameters "the gravitational mass M, the rotation a, and the NUT L." The vierbein field is axially symmetric, and the associated metric gives the Kerr-Taub-NUT spacetime. Calculation of the total energy using two different methods, the gravitational energy momentum and the Riemannian connection 1-form Γ α β , is carried out. It is shown that the two methods give the same results of energy and momentum. The value of energy is shown to depend on the mass M and the NUT parameter L. If L is vanishing, then the total energy reduced to the energy of Kerr black hole
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