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.

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.

Wormhole solutions in embedding class 1 space–time

2021 ◽  
Vol 36 (02) ◽  
pp. 2150015
Author(s):  
Nayan Sarkar ◽  
Susmita Sarkar ◽  
Farook Rahaman ◽  
Safiqul Islam
Keyword(s):  
Dimensional Space ◽  
Vacuum Solution ◽  
Energy Condition ◽  
Radial Distance ◽  
Space Time ◽  
Exotic Matter ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Asymptotically Flat ◽  
Class 1

The present work looks for new spherically symmetric wormhole solutions of the Einstein field equations based on the well-known embedding class 1, i.e. Karmarkar condition. The embedding theorems have an interesting property that connects an [Formula: see text]-dimensional space–time to the higher-dimensional Euclidean flat space–time. The Einstein field equations yield the wormhole solution by violating the null energy condition (NEC). Here, wormholes solutions are obtained corresponding to three different redshift functions: rational, logarithm, and inverse trigonometric functions, in embedding class 1 space–time. The obtained shape function in each case satisfies the flare-out condition after the throat radius, i.e. good enough to represents wormhole structure. In cases of WH1 and WH2, the solutions violate the NEC as well as strong energy condition (SEC), i.e. here the exotic matter content exists within the wormholes and strongly sustains wormhole structures. In the case of WH3, the solution violates NEC but satisfies SEC, so for violating the NEC wormhole preserve due to the presence of exotic matter. Moreover, WH1 and WH2 are asymptotically flat while WH3 is not asymptotically flat. So, indeed, WH3 cutoff after some radial distance [Formula: see text], the Schwarzschild radius, and match to the external vacuum solution.

PLANE SYMMETRIC VISCOUS-FLUID COSMOLOGICAL MODELS WITH HEAT FLUX

1994 ◽  
Vol 03 (03) ◽  
pp. 639-645
Author(s):  
L.K. PATEL ◽  
LAKSHMI S. DESAI
Keyword(s):  
Heat Flux ◽  
Viscous Fluid ◽  
Vacuum Solution ◽  
Big Bang ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Plane Symmetric ◽  
Inhomogeneous Plane ◽  
Physical Features ◽  
Big Bang Singularity

A class of nonstatic inhomogeneous plane-symmetric solutions of Einstein field equations is obtained. The source for these solutions is a viscous fluid with heat flow. The fluid flow is irrotational and it has nonzero expansion, shear and acceleration. All these solutions have a big-bang singularity. The matter-free limit of the solutions is the well-known Kasner vacuum solution. Some physical features of the solutions are briefly discussed.

scholarly journals Axially Symmetric Null Dust Space-Time, Naked Singularity, and Cosmic Time Machine

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Faizuddin Ahmed
Keyword(s):  
Gravitational Lensing ◽  
Cosmic Time ◽  
Naked Singularity ◽  
Space Time ◽  
Axially Symmetric ◽  
Time Machine ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Closed Orbits ◽  
Group A

We present a gravitational collapse null dust solution of the Einstein field equations. The space-time is regular everywhere except on the symmetry axis where it possesses a naked curvature singularity and admits one parameter isometry group, a generator of axial symmetry along the cylinder which has closed orbits. The space-time admits closed timelike curves (CTCs) which develop at some particular moment in a causally well-behaved manner and may represent a Cosmic Time Machine. The radial geodesics near the singularity and the gravitational lensing (GL) will be discussed. The physical interpretation of this solution, based on the study of the equation of the geodesic deviation, will be presented. It was demonstrated that this solution depends on the local gravitational field consisting of two components with amplitudes Ψ2 and Ψ4.

scholarly journals On the equivalence of approximate stationary axially symmetric solutions of the Einstein field equations

2016 ◽  
Vol 22 (4) ◽  
pp. 305-311 ◽  
Author(s):  
Kuantay Boshkayev ◽  
Hernando Quevedo ◽  
Saken Toktarbay ◽  
Bakytzhan Zhami ◽  
Medeu Abishev
Keyword(s):  
Axially Symmetric ◽  
Einstein Field Equations ◽  
Field Equations

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.

Weyl static axially symmetric field equations in modified f(T) gravity

2017 ◽  
Vol 14 (04) ◽  
pp. 1750053 ◽  
Author(s):  
Saeed Nayeh ◽  
Mehrdad Ghominejad
Keyword(s):  
General Relativity ◽  
Symmetric Space ◽  
Energy Momentum Tensor ◽  
Radial Component ◽  
Momentum Tensor ◽  
Space Time ◽  
Axially Symmetric ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Torsion Scalar

In this paper, we obtain the field equations of Weyl static axially symmetric space-time in the framework of [Formula: see text] gravity, where [Formula: see text] is torsion scalar. We will see that, for [Formula: see text] related to teleparallel equivalent general relativity, these equations reduce to Einstein field equations. We show that if the components of energy–momentum tensor are symmetric, the scalar torsion must be either constant or only a function of radial component [Formula: see text]. The solutions of some functions [Formula: see text] in which [Formula: see text] is a function of [Formula: see text] are obtained.

scholarly journals Reciprocal NUT spacetimes

2015 ◽  
Vol 12 (09) ◽  
pp. 1550083
Author(s):  
Davood Momeni ◽  
Surajit Chattopadhyay ◽  
Ratbay Myrzakulov
Keyword(s):  
Vacuum Solution ◽  
Static Solution ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Disk Model ◽  
Static Vacuum ◽  
Stationary Spacetime ◽  
Time Space ◽  
Spherically Symmetric Solution ◽  
Stationary Spacetimes

In this paper, we study the Ehlers' transformation (sometimes called gravitational duality rotation) for reciprocal static metrics. First, we introduce the concept of reciprocal metric. We prove a theorem which shows how we can construct a certain new static solution of Einstein field equations using a seed metric. Later, we investigate the family of stationary spacetimes of such reciprocal metrics. The key here is a theorem from Ehlers', which relates any static vacuum solution to a unique stationary metric. The stationary metric has a magnetic charge. The spacetime represents Newman-Unti-Tamburino (NUT) solutions. Since any stationary spacetime can be decomposed into a 1 + 3 time-space decomposition, Einstein field equations for any stationary spacetime can be written in the form of Maxwell's equations for gravitoelectromagnetic fields. Further, we show that this set of equations is invariant under reciprocal transformations. An additional point is that the NUT charge changes the sign. As an instructive example, by starting from the reciprocal Schwarzschild as a spherically symmetric solution and reciprocal Morgan–Morgan disk model as seed metrics we find their corresponding stationary spacetimes. Starting from any static seed metric, performing the reciprocal transformation and by applying an additional Ehlers' transformation we obtain a family of NUT spaces with negative NUT factor (reciprocal NUT factors).

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