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.

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.

SEPARATING STATIONARY AXIALLY-SYMMETRIC ASYMPTOTICALLY FLAT METRICS

1989 ◽  
Vol 04 (12) ◽  
pp. 2953-2958 ◽  
Author(s):  
Z. YA. TURAKULOV
Keyword(s):  
Gordon Equation ◽  
Separation Of Variables ◽  
Vacuum Solution ◽  
Complete Separation ◽  
Kerr Metric ◽  
Axially Symmetric ◽  
Spherical System ◽  
Asymptotically Flat ◽  
Klein Gordon ◽  
Klein Gordon Equation

Stationary axially-symmetric asymptotically flat metrics allowing the complete separation of variables in the Klein-Gordon equation are considered. It is shown that if such metrics coincide at infinity with the metric of spherical system of coordinates, the variables for them in the Einstein equation are completely separable and the only vacuum solution is the Kerr metric.

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.

scholarly journals Axial Symmetry Cosmological Constant Vacuum Solution of Field Equations with a Curvature Singularity, Closed Time-Like Curves, and Deviation of Geodesics

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Faizuddin Ahmed ◽  
Bidyut Bikash Hazarika ◽  
Debojit Sarma
Keyword(s):  
Cosmological Constant ◽  
Vacuum Solution ◽  
Space Time ◽  
Axially Symmetric ◽  
De Sitter ◽  
Curvature Singularity ◽  
Field Equations ◽  
Type D ◽  
Initial Space ◽  
Coulomb Type

In this paper, we present a type D, nonvanishing cosmological constant, vacuum solution of Einstein’s field equations, extension of an axially symmetric, asymptotically flat vacuum metric with a curvature singularity. The space-time admits closed time-like curves (CTCs) that appear after a certain instant of time from an initial space-like hypersurface, indicating it represents a time-machine space-time. We wish to discuss the physical properties and show that this solution can be interpreted as gravitational waves of Coulomb-type propagate on anti-de Sitter space backgrounds. Our treatment focuses on the analysis of the equation of geodesic deviations.

scholarly journals Distinguishing Brans–Dicke–Kerr type naked singularities and black holes with their thin disk electromagnetic radiation properties

2020 ◽  
Vol 80 (2) ◽  
Author(s):  
Shahab Shahidi ◽  
Tiberiu Harko ◽  
Zoltán Kovács
Keyword(s):  
Black Holes ◽  
Comparative Investigation ◽  
Compact Objects ◽  
Electromagnetic Properties ◽  
Kerr Metric ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Axially Symmetric ◽  
Field Equations ◽  
Naked Singularities

Abstract The possible existence of naked singularities, hypothetical astrophysical objects, characterized by a gravitational singularity without an event horizon is still an open problem in present day astrophysics. From an observational point of view distinguishing between astrophysical black holes and naked singularities also represents a major challenge. One possible way of differentiating naked singularities from black holes is through the comparative study of thin accretion disks properties around these different types of compact objects. In the present paper we continue the comparative investigation of accretion disk properties around axially-symmetric rotating geometries in Brans–Dicke theory in the presence of a massless scalar field. The solution of the field equations contains the Kerr metric as a particular case, and, depending on the numerical values of the model parameter $$\gamma $$γ, has also solutions corresponding to non-trivial black holes and naked singularities, respectively. Due to the differences in the exterior geometries between black holes and Brans–Dicke–Kerr naked singularities, the thermodynamic and electromagnetic properties of the disks (energy flux, temperature distribution and equilibrium radiation spectrum) are different for these two classes of compact objects, consequently giving clear observational signatures that could discriminate between black holes and naked singularities.

scholarly journals A STATIONARY VACUUM SOLUTION DUAL TO THE KERR SOLUTION

2001 ◽  
Vol 16 (30) ◽  
pp. 1959-1962 ◽  
Author(s):  
Z. YA. TURAKULOV ◽  
N. DADHICH
Keyword(s):  
Dimensionless Parameter ◽  
Mass Parameter ◽  
Vacuum Solution ◽  
Kerr Solution ◽  
Radial Coordinate ◽  
Axially Symmetric ◽  
Massless Limit ◽  
Metric Functions ◽  
Two Parameter ◽  
Nut Solution

We present a stationary axially symmetric two-parameter vacuum solution which could be considered as "dual" to the Kerr solution. It is obtained by removing the mass parameter from the function of the radial coordinate and introducing a dimensionless parameter in the function of the angle coordinate in the metric functions. It turns out that it is in fact the massless limit of the Kerr–NUT solution.

The Kerr solution

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Kerr Black Hole ◽  
Geodesic Equation ◽  
Einstein Equations ◽  
Kerr Metric ◽  
Kerr Solution ◽  
Axially Symmetric ◽  
Observable Universe ◽  
Einstein Vacuum Equations ◽  
Einstein Vacuum ◽  
The Many

This chapter covers the Kerr metric, which is an exact solution of the Einstein vacuum equations. The Kerr metric provides a good approximation of the spacetime near each of the many rotating black holes in the observable universe. This chapter shows that the Einstein equations are nonlinear. However, there exists a class of metrics which linearize them. It demonstrates the Kerr–Schild metrics, before arriving at the Kerr solution in the Kerr–Schild metrics. Since the Kerr solution is stationary and axially symmetric, this chapter shows that the geodesic equation possesses two first integrals. Finally, the chapter turns to the Kerr black hole, as well as its curvature singularity, horizons, static limit, and maximal extension.

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