scholarly journals Regularization off(T)Gravity Theories and Local Lorentz Transformation

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Gamal G. L. Nashed
Keyword(s):  
Lorentz Transformation ◽  
Arbitrary Function ◽  
Spherical Symmetry ◽  
Gravitational Theory ◽  
Radial Coordinate ◽  
Field Equations ◽  
Tetrad Field ◽  
Local Lorentz Transformation ◽  
Gravity Theories

We regularized the field equations off(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 off(T)gravitational theory (which are not invariant under LLT). This “general tetrad field” is then applied to the regularized field equations off(T). We show that the effect of the arbitrary function which is involved in the LLT invariably disappears.

Fixing redundant degrees of teleparallel equivalent of general relativity

2017 ◽  
Vol 14 (11) ◽  
pp. 1750154
Author(s):  
Gamal G. L. Nashed ◽  
B. Elkhatib
Keyword(s):  
General Relativity ◽  
Lorentz Transformation ◽  
Arbitrary Function ◽  
Degrees Of Freedom ◽  
Symmetric Tensor ◽  
Cylindrical Symmetry ◽  
Radial Coordinate ◽  
Field Equations ◽  
Local Lorentz Transformation ◽  
Teleparallel Theory

It is well known that the field equation of teleparallel theory which is equivalent to general relativity completely agrees with the field equations of general relativity. However, teleparallel equivalent of general relativity has six redundant degrees of freedom which spoil the true physics. These extra degrees are related to the local Lorentz transformation. In this study, we give three different tetrad fields having cylindrical symmetry and depend only on the radial coordinate. One of these tetrads contains an arbitrary function, which is responsible to reproduce the other solutions, which come from local Lorentz transformation. We show by explicate calculations that this arbitrary function spoils the calculations of the conserved charges. We formulate a skew-symmetric tensor whose vanishing value puts a constraint on this arbitrary function. This constraint fixed the redundant degrees of freedom which characterize the teleparallel equivalent of general relativity.

scholarly journals Axially Symmetric-dS Solution in Teleparallelf(T)Gravity Theories

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Gamal G. L. Nashed
Keyword(s):  
Differential Equation ◽  
Ricci Tensor ◽  
Torsion Tensor ◽  
Vacuum Solution ◽  
Axially Symmetric ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Tetrad Field ◽  
Local Lorentz Transformation ◽  
Gravity Theories

We 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 angleϕand get a new tetrad field. Using this tetrad, we get a differential equation from the scalar torsionT=TαμνSαμν. Solving this differential equation we obtain a solution to thef(T)gravity theories under certain conditions on the form off(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.

scholarly journals Exact Axially Symmetric Solution inf(T)Gravity Theory

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Gamal G. L. Nashed
Keyword(s):  
Vacuum Solution ◽  
Gravity Theory ◽  
Kerr Metric ◽  
Radial Coordinate ◽  
Lorentz Transformations ◽  
Axially Symmetric ◽  
Field Equations ◽  
Tetrad Field ◽  
Kerr Spacetime ◽  
Euler’S Angles

A general tetrad field with sixteen unknown functions is applied to the field equations off(T)gravity theory. An analytic vacuum solution is derived with two constants of integration and an angleΦthat depends on the angle coordinateϕand radial coordinater. The tetrad field of this solution is axially symmetric and the scalar torsion vanishes. We calculate the associated metric of the derived solution and show that it represents Kerr spacetime. Finally, we show that the derived solution can be described by two local Lorentz transformations in addition to a tetrad field that is the square root of the Kerr metric. One of these local Lorentz transformations is a special case of Euler’s angles and the other represents a boost when the rotation parameter vanishes.

Kerr–Newman solution in modified teleparallel theory of gravity

2014 ◽  
Vol 24 (01) ◽  
pp. 1550007 ◽  
Author(s):  
Gamal G. L. Nashed
Keyword(s):  
Azimuthal Angle ◽  
Polar Angle ◽  
Radial Coordinate ◽  
Lorentz Transformations ◽  
Square Root ◽  
Axially Symmetric ◽  
Field Equations ◽  
Tetrad Field ◽  
Teleparallel Theory ◽  
Theory Of Gravity

A nondiagonal tetrad field having six unknown functions plus an angle Φ, which is a function of the radial coordinate r, azimuthal angle θ and the polar angle ϕ, is applied to the charged field equations of modified teleparallel theory of gravity. A special nonvacuum solution is derived with three constants of integration. The tetrad field of this solution is axially symmetric and its scalar torsion is constant. The associated metric of the derived solution gives Kerr–Newman spacetime. We have shown that the derived solution can be described by a local Lorentz transformations plus a diagonal tetrad field that is the square root of the Kerr–Newman metric. We show that any solution of general relativity (GR) can be a solution in f(T) under certain conditions.

scholarly journals Stable and self-consistent compact star models in teleparallel gravity

2020 ◽  
Vol 80 (10) ◽  
Author(s):  
G. G. L. Nashed ◽  
S. Capozziello
Keyword(s):  
Compact Star ◽  
Vacuum Solution ◽  
Radial Pressure ◽  
Teleparallel Gravity ◽  
Compact Objects ◽  
Radial Coordinate ◽  
Model Parameters ◽  
Field Equations ◽  
Tetrad Field ◽  
Star Models

AbstractIn the framework of Teleparallel Gravity, we derive a charged non-vacuum solution for a physically symmetric tetrad field with two unknown functions of radial coordinate. The field equations result in a closed-form adopting particular metric potentials and a suitable anisotropy function combined with the charge. Under these circumstances, it is possible to obtain a set of configurations compatible with observed pulsars. Specifically, boundary conditions for the interior spacetime are applied to the exterior Reissner–Nordström metric to constrain the radial pressure that has to vanish through the boundary. Starting from these considerations, we are able to fix the model parameters. The pulsar $$\textit{PSR J 1614-2230}$$ PSR J 1614 - 2230 , with estimated mass $$M= 1.97 \pm 0.04\, M_{\circledcirc },$$ M = 1.97 ± 0.04 M ⊚ , and radius $$R= 9.69 \pm 0.2$$ R = 9.69 ± 0.2 km is used to test numerically the model. The stability is studied, through the causality conditions and adiabatic index, adopting the Tolman–Oppenheimer–Volkov equation. The mass–radius (M, R) relation is derived. Furthermore, the compatibility of the model with other observed pulsars is also studied. We reasonably conclude that the model can represent realistic compact objects.

scholarly journals Spherically Symmetric Solution in (1+4)-Dimensionalf(T)Gravity Theories

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Gamal G. L. Nashed
Keyword(s):  
Symmetric Solution ◽  
Vacuum Solution ◽  
Azimuthal Angle ◽  
Radial Coordinate ◽  
Spherically Symmetric ◽  
Field Equations ◽  
Tetrad Field ◽  
The Third ◽  
Special Vacuum ◽  
Spherically Symmetric Solution

A nondiagonal spherically symmetric tetrad field, involving four unknown functions of radial coordinaterplus an angleΦ, which is a generalization of the azimuthal angleϕ, is applied to the field equations of (1+4)-dimensionalf(T)gravity theory. A special vacuum solution with one constant of integration is derived. The physical meaning of this constant is shown to be related to the gravitational mass of the system and the associated metric represents Schwarzschild in (1+4)-dimension. The scalar torsion related to this solution vanishes. We put the derived solution in a matrix form and rewrite it as a product of three matrices: the first represents a rotation while the second represents an inertia and the third matrix is the diagonal square root of Schwarzschild spacetime in (1+4)-dimension.

The Field Equations of Metric-Affine Gravitational Theories

1978 ◽  
Vol 33 (4) ◽  
pp. 398-401 ◽  
Author(s):  
S. J. Aldersley
Keyword(s):  
Vector Potential ◽  
Gravitational Theory ◽  
Field Equations ◽  
Gravitational Theories ◽  
Special Case ◽  
Potential Conditions

The notions of conservation of charge and dimensional consistency are used to obtain conditions which uniquely characterize the field equations of electromagnetism and gravitation in a metric-affine gravitational framework with a vector potential. Conditions for the uniqueness of the choice of field equations of a metric-affine gravitational theory (in the absence of electromagnetism) follow as a special case. Some consequences are discussed.

scholarly journals A MAXWELL-LIKE FORMULATION OF GRAVITATIONAL THEORY IN MINKOWSKI SPACE–TIME

2007 ◽  
Vol 16 (06) ◽  
pp. 1027-1041 ◽  
Author(s):  
EDUARDO A. NOTTE-CUELLO ◽  
WALDYR A. RODRIGUES
Keyword(s):  
Gravitational Field ◽  
Minkowski Space ◽  
Gravitational Theory ◽  
Space Time ◽  
Lorentzian Geometry ◽  
Field Equations ◽  
Yang Mills ◽  
Minkowski Space Time ◽  
Clifford Bundle ◽  
Gauge Fixing

Using the Clifford bundle formalism, a Lagrangian theory of the Yang–Mills type (with a gauge fixing term and an auto interacting term) for the gravitational field in Minkowski space–time is presented. It is shown how two simple hypotheses permit the interpretation of the formalism in terms of effective Lorentzian or teleparallel geometries. In the case of a Lorentzian geometry interpretation of the theory, the field equations are shown to be equivalent to Einstein's equations.

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