Teleparallel gravity with non-vanishing curvature

2018 ◽  
Vol 96 (12) ◽  
pp. 1373-1383 ◽  
Author(s):  
M.I. Wanas ◽  
Samah A. Ammar ◽  
Shymaa A. Refaey
Keyword(s):  
Linear Connection ◽  
Main Idea ◽  
Building Blocks ◽  
Teleparallel Gravity ◽  
Field Equations ◽  
Exterior Field ◽  
Weak Equivalence Principle ◽  
Absolute Parallelism ◽  
Pure Gravity ◽  
Curvature And Torsion

Guided by the rules of Einstein’s geometrization philosophy, a pure geometric field theory is constructed. The Lagrangian used to derive the field equations of the theory is a curvature scalar of a version of absolute parallelism (AP) geometry known in the literature as the parameterized absolute parallelism (PAP) geometry. The linear connection of this version has simultaneously non-vanishing curvature and torsion. Analysis of the theory obtained shows clearly that it is a pure gravity theory. The theory is a teleparallel one, since the building blocks of both PAP and AP geometries are the same. It is shown analytically that the theory has a trivial version in the AP-geometry, if gravity is attributed to curvature not to torsion. In the case of spherical symmetry, solutions of the field equations give rise to the Schwarzschild exterior field. The theory depends on two principles: covariance and unification. The weak equivalence principle is satisfied under a certain condition. The work preserves Einstein’s main idea that gravity is just space–time curvature, although it is not a metric theory. It is shown that the theory reduces to vacuum general relativity upon taking the parameter of the geometry b = 0.

scholarly journals SPACETIME STRUCTURE AND ELECTROMAGNETISM

2010 ◽  
Vol 25 (20) ◽  
pp. 1705-1721 ◽  
Author(s):  
M. I. WANAS ◽  
SAMAH. A. AMMAR
Keyword(s):  
Geometric Object ◽  
The Other ◽  
Field Theories ◽  
Necessary Condition ◽  
Geometric Representation ◽  
Lagrangian Functions ◽  
Absolute Parallelism ◽  
Spacetime Structure ◽  
Pure Gravity ◽  
Curvature And Torsion

Two Lagrangian functions are used to construct geometric field theories. One of these Lagrangians depends on the curvature of space, while the other depends on curvature and torsion. It is shown that the theory constructed from the first Lagrangian gives rise to pure gravity, while the theory constructed using the second Lagrangian gives rise to both gravity and electromagnetism. The two theories are constructed in a version of absolute parallelism geometry in which both curvature and torsion are, simultaneously, nonvanishing. One single geometric object, W-tensor, reflecting the properties of curvature and torsion, is defined in this version and is used to construct the second theory. The main conclusion is that a necessary condition for geometric representation of electromagnetism is the presence of a nonvanishing torsion in the geometry used.

scholarly journals A Field Theory with Curvature and Anticurvature

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
M. I. Wanas ◽  
Mona M. Kamal
Keyword(s):  
Field Theory ◽  
Free Space ◽  
Unified Field Theory ◽  
Field Equations ◽  
Weak Equivalence Principle ◽  
Unified Field ◽  
Special Cases ◽  
Geometric Objects ◽  
Pure Gravity ◽  
Physical Quantities

The present work is an attempt to construct a unified field theory in a space with curvature and anticurvature, the PAP-space. The theory is derived from an action principle and a Lagrangian density using a symmetric linear parameterized connection. Three different methods are used to explore physical contents of the theory obtained. Poisson’s equations for both material and charge distributions are obtained, as special cases, from the field equations of the theory. The theory is a pure geometric one in the sense that material distribution, charge distribution, gravitational and electromagnetic potentials, and other physical quantities are defined in terms of pure geometric objects of the structure used. In the case of pure gravity in free space, the spherical symmetric solution of the field equations gives the Schwarzschild exterior field. The weak equivalence principle is respected only in the case of pure gravity in free space; otherwise it is violated.

scholarly journals EXTENDED ABSOLUTE PARALLELISM GEOMETRY

2008 ◽  
Vol 05 (07) ◽  
pp. 1109-1135 ◽  
Author(s):  
NABIL. L. YOUSSEF ◽  
A. M. SID-AHMED
Keyword(s):  
Tangent Bundle ◽  
Special Form ◽  
Vector Fields ◽  
A Priori ◽  
Building Blocks ◽  
Absolute Parallelism ◽  
Linearly Independent ◽  
Geometric Objects ◽  
Directional Argument ◽  
Curvature Tensors

In this paper, we study Absolute Parallelism (AP-) geometry on the tangent bundle TM of a manifold M. Accordingly, all geometric objects defined in this geometry are not only functions of the positional argument x, but also depend on the directional argument y. Moreover, many new geometric objects, which have no counterpart in the classical AP-geometry, emerge in this different framework. We refer to such a geometry as an Extended Absolute Parallelism (EAP-) geometry. The building blocks of the EAP-geometry are a nonlinear connection (assumed given a priori) and 2n linearly independent vector fields (of special form) defined globally on TM defining the parallelization. Four different d-connections are used to explore the properties of this geometry. Simple and compact formulae for the curvature tensors and the W-tensors of the four defined d-connections are obtained, expressed in terms of the torsion and the contortion tensors of the EAP-space. Further conditions are imposed on the canonical d-connection assuming that it is of Cartan type (resp. Berwald type). Important consequences of these assumptions are investigated. Finally, a special form of the canonical d-connection is studied under which the classical AP-geometry is recovered naturally from the EAP-geometry. Physical aspects of some of the geometric objects investigated are pointed out and possible physical implications of the EAP-space are discussed, including an outline of a generalized field theory on the tangent bundle TM of M.

Unified Field Theory

1950 ◽  
Vol 2 ◽  
pp. 427-439 ◽  
Author(s):  
Max Wyman
Keyword(s):  
Field Theory ◽  
Variational Principle ◽  
Electromagnetic Fields ◽  
Linear Connection ◽  
Hamiltonian Function ◽  
Unified Theory ◽  
Unified Field Theory ◽  
Field Equations ◽  
Unified Field

Introduction. In a recent unified theory originated by Einstein and Straus [l], the gravitational and electromagnetic fields are represented by a single nonsymmetric tensor gy which is a function of four coordinates xr(r = 1, 2, 3, 4). In addition a non-symmetric linear connection Γjki is assumed for the space and a Hamiltonian function is defined in terms of gij and Γjki. By means of a variational principle in which the gij and Γjki are allowed to vary independently the field equations are obtained and can be written(0.1)(0.2)(0.3)(0.4)

scholarly journals Accelerating Universe with Viscous Cosmic String in Quadratic Form of Teleparallel Gravity

2019 ◽  
Vol 11 (3) ◽  
pp. 249-262
Author(s):  
S. R. Bhoyar ◽  
V. R. Chirde ◽  
S. H. Shekh
Keyword(s):  
Cosmic String ◽  
Teleparallel Gravity ◽  
Negative Slope ◽  
Accelerating Universe ◽  
Field Equations ◽  
Physical Behavior ◽  
Torsion Scalar ◽  
Bulk Viscous ◽  
The Universe ◽  
Physical Quantities

In this paper, we have investigated Kantowaski-Sachs cosmological model with bulk viscous and cosmic string in the framework of Teleparallel Gravity so called f(T) gravity, where T denotes the torsion scalar. The behavior of accelerating universe is discussed towards the particular choice of f(T) = Α(T) + β(T)m. The exact solutions of the field equations are obtained by applying variable deceleration parameter which is linear in time with a negative slope. The physical behavior of these models has been discussed using some physical quantities. Also, the function of the torsion scalar for the universe is evaluated.

scholarly journals A duality between curvature and torsion

2018 ◽  
Vol 27 (14) ◽  
pp. 1847008 ◽  
Author(s):  
Swanand Khanapurkar ◽  
Tejinder P. Singh
Keyword(s):  
Scale Effects ◽  
Gravitational Interaction ◽  
Large Mass ◽  
Small Mass ◽  
Teleparallel Gravity ◽  
Einstein Equations ◽  
Small Scale ◽  
Underlying Theory ◽  
Newman Black Hole ◽  
Curvature And Torsion

Compton wavelength and Schwarzschild radius are considered here as limiting cases of a unified length scale. Using this length, it is shown that the Dirac equation and the Einstein equations for a point mass are limiting cases of an underlying theory which includes torsion. We show that in this underlying theory, the gravitational interaction between small masses is weaker than in Newtonian gravity. We explain as to why the Kerr–Newman black hole and the electron both have the same nonclassical gyromagnetic ratio. We propose a duality between curvature and torsion and show that general relativity and teleparallel gravity are respectively the large mass and small mass limit of the ECSK theory. We demonstrate that small scale effects of torsion can be tested with current technology.

Wormhole in 5D Kaluza–Klein cosmology

2017 ◽  
Vol 32 (07) ◽  
pp. 1750023 ◽  
Author(s):  
Gargi Biswas ◽  
B. Modak
Keyword(s):  
Boundary Conditions ◽  
Cosmological Constant ◽  
Dimensional Reduction ◽  
Dimensional Space ◽  
Field Equations ◽  
Positive Cosmological Constant ◽  
Euclidean Field ◽  
Pure Gravity ◽  
Imaginary Field ◽  
Kaluza Klein

We present wormhole as a solution of Euclidean field equations as well as the solution of the Wheeler–deWitt (WD) equation satisfying Hawking–Page wormhole boundary conditions in (4 + 1)-dimensional Kaluza–Klein cosmology. The wormholes are considered in the cases of pure gravity, minimally coupled scalar (imaginary) field and with a positive cosmological constant assuming dynamical extra-dimensional space. In above cases, wormholes are allowed both from Euclidean field equations and WD equation. The dimensional reduction is possible.

scholarly journals THE SEIBERG–WITTEN MAP FOR NON-COMMUTATIVE PURE GRAVITY AND VACUUM MAXWELL THEORY

2013 ◽  
Vol 10 (06) ◽  
pp. 1350023 ◽  
Author(s):  
ELISABETTA DI GREZIA ◽  
GIAMPIERO ESPOSITO ◽  
MARCO FIGLIOLIA ◽  
PATRIZIA VITALE
Keyword(s):  
Explicit Construction ◽  
Einstein Equations ◽  
Electromagnetic Potential ◽  
Field Equations ◽  
Maxwell Theory ◽  
Commutative Field ◽  
Yang Mills ◽  
First Order ◽  
Pure Gravity ◽  
Vacuum Solutions

In this paper the Seiberg–Witten map is first analyzed for non-commutative Yang–Mills theories with the related methods, developed in the literature, for its explicit construction, that hold for any gauge group. These are exploited to write down the second-order Seiberg–Witten map for pure gravity with a constant non-commutativity tensor. In the analysis of pure gravity when the classical space–time solves the vacuum Einstein equations, we find for three distinct vacuum solutions that the corresponding non-commutative field equations do not have solution to first order in non-commutativity, when the Seiberg–Witten map is eventually inserted. In the attempt of understanding whether or not this is a peculiar property of gravity, in the second part of the paper, the Seiberg–Witten map is considered in the simpler case of Maxwell theory in vacuum in the absence of charges and currents. Once more, no obvious solution of the non-commutative field equations is found, unless the electromagnetic potential depends in a very special way on the wave vector.

scholarly journals NON-COMMUTATIVE EINSTEIN EQUATIONS AND SEIBERG–WITTEN MAP

2011 ◽  
Vol 03 ◽  
pp. 143-149 ◽  
Author(s):  
PAOLO ASCHIERI ◽  
ELISABETTA DI GREZIA ◽  
GIAMPIERO ESPOSITO
Keyword(s):  
Field Theory ◽  
Einstein Equations ◽  
Action Functional ◽  
Field Equations ◽  
Commutative Field ◽  
First Order ◽  
Classical Geometry ◽  
Pure Gravity

The Seiberg–Witten map is a powerful tool in non-commutative field theory, and it has been recently obtained in the literature for gravity itself, to first order in non-commutativity. This paper, relying upon the pure-gravity form of the action functional considered in Ref. 2, studies the expansion to first order of the non-commutative Einstein equations, and whether the Seiberg–Witten map can lead to a solution of such equations when the underlying classical geometry is Schwarzschild. We find that, if one first obtains the non-commutative field equations by varying the action of Ref. 2 with respect to all non-commutative fields, and then tries to solve these equations by expressing the non-commutative fields in terms of the commutative ones via Seiberg–Witten map, no solution of these equations can be obtained when the commutative background is Schwarzschild.

GENERALIZED GRAVITY IN CLIFFORD SPACES, VACUUM ENERGY AND GRAND UNIFICATION

2011 ◽  
Vol 08 (06) ◽  
pp. 1239-1258 ◽  
Author(s):  
CARLOS CASTRO
Keyword(s):  
Cosmological Constant ◽  
Gauge Field ◽  
Constant Term ◽  
Gauge Field Theories ◽  
Field Equations ◽  
Spectral Action ◽  
Action Model ◽  
The One ◽  
Curvature And Torsion ◽  
Vacuum Solutions

Polyvector-valued gauge field theories in Clifford spaces are used to construct a novel Cl (3, 2) gauge theory of gravity that furnishes modified curvature and torsion tensors leading to important modifications of the standard gravitational action with a cosmological constant. Vacuum solutions exist which allow a cancelation of the contributions of a very large cosmological constant term and the extra terms present in the modified field equations. Generalized gravitational actions in Clifford-spaces are provided and some of their physical implications are discussed. It is shown how the 16 fermions and their masses in each family can be accommodated within a Cl (4) gauge field theory. In particular, the Higgs fields admit a natural Clifford-space interpretation that differs from the one in the Chamseddine–Connes spectral action model of non-commutative geometry. We finalize with a discussion on the relationship with the Pati–Salam color-flavor model group SU (4)C × SU (4)F and its symmetry breaking patterns. An Appendix is included with useful Clifford algebraic relations.

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