scholarly journals SYMMETRIC TELEPARALLEL GRAVITY: SOME EXACT SOLUTIONS AND SPINOR COUPLINGS

2013 ◽  
Vol 28 (32) ◽  
pp. 1350167 ◽  
Author(s):  
MUZAFFER ADAK ◽  
ÖZCAN SERT ◽  
MESTAN KALAY ◽  
MURAT SARI
Keyword(s):  
Riemannian Space ◽  
Tangent Vector ◽  
Teleparallel Gravity ◽  
Coupling Coefficients ◽  
Field Equations ◽  
Minimal Coupling ◽  
Zero Curvature ◽  
Pp Wave ◽  
Teleparallel Theory ◽  
Parallel Transportation

In this paper, we elaborate on the symmetric teleparallel gravity (STPG) written in a non-Riemannian space–time with nonzero nonmetricity, but zero torsion and zero curvature. First, we give a prescription for obtaining the nonmetricity from the metric in a peculiar gauge. Then, we state that under a novel prescription of parallel transportation of a tangent vector in this non-Riemannian geometry, the autoparallel curves coincide with those of the Riemannian space–times. Subsequently, we represent the symmetric teleparallel theory of gravity by the most general quadratic and parity conserving Lagrangian with lagrange multipliers for vanishing torsion and curvature. We show that our Lagrangian is equivalent to the Einstein–Hilbert Lagrangian for certain values of coupling coefficients. Thus, we arrive at calculating the field equations via independent variations. Then, we obtain in turn conformal, spherically symmetric static, cosmological and pp-wave solutions exactly. Finally, we discuss a minimal coupling of a spin-1/2 field to STPG.

scholarly journals Minimal coupling in presence of non-metricity and torsion

2020 ◽  
Vol 80 (8) ◽  
Author(s):  
Adrià Delhom
Keyword(s):  
Riemannian Space ◽  
Field Equations ◽  
Lagrange Equations ◽  
Minimal Coupling ◽  
Covariant Derivatives ◽  
Derivatives Of ◽  
Matter Fields

Abstract We deal with the question of what it means to define a minimal coupling prescription in presence of torsion and/or non-metricity, carefully explaining while the naive substitution $$\partial \rightarrow \nabla $$∂→∇ introduces extra couplings between the matter fields and the connection that can be regarded as non-minimal in presence of torsion and/or non-metricity. We will also investigate whether minimal coupling prescriptions at the level of the action (MCPL) or at the level of field equations (MCPF) lead to different dynamics. To that end, we will first write the Euler–Lagrange equations for matter fields in terms of the covariant derivatives of a general non-Riemannian space, and derivate the form of the associated Noether currents and charges. Then we will see that if the minimal coupling prescriptions is applied as we discuss, for spin 0 and 1 fields the results of MCPL and MCPF are equivalent, while for spin 1/2 fields there is a difference if one applies the MCPF or the MCPL, since the former leads to charge violation.

scholarly journals Scalar perturbation potentials in a homogeneous and isotropic Weitzenböck geometry

2016 ◽  
Vol 25 (07) ◽  
pp. 1650087
Author(s):  
A. Behboodi ◽  
S. Akhshabi ◽  
K. Nozari
Keyword(s):  
Degrees Of Freedom ◽  
Teleparallel Gravity ◽  
Scalar Perturbation ◽  
Coordinate Frame ◽  
Field Equations ◽  
Tetrad Field ◽  
Cosmological Perturbation ◽  
Gauge Invariant ◽  
Teleparallel Theory ◽  
Perturbation Parameters

We describe the fully gauge invariant cosmological perturbation equations in teleparallel gravity by using the gauge covariant version of the Stewart lemma for obtaining the variations in tetrad perturbations. In teleparallel theory, perturbations are the result of small fluctuations in the tetrad field. The tetrad transforms as a vector in both its holonomic and anholonomic indices. As a result, in the gauge invariant formalism, physical degrees of freedom are those combinations of perturbation parameters which remain invariant under a diffeomorphism in the coordinate frame, followed by an arbitrary rotation of the local inertial (Lorentz) frame. We derive these gauge invariant perturbation potentials for scalar perturbations and present the gauge invariant field equations governing their evolution.

scholarly journals FERMIONIC AND SCALAR FIELDS AS SOURCES OF INTERACTING DARK MATTER–DARK ENERGY

2011 ◽  
Vol 20 (13) ◽  
pp. 2543-2558 ◽  
Author(s):  
SAMUEL LEPE ◽  
JAVIER LORCA ◽  
FRANCISCO PEÑA ◽  
YERKO VÁSQUEZ
Keyword(s):  
Dark Matter ◽  
Dark Energy ◽  
Scalar Field ◽  
Analytical Solution ◽  
Scalar Fields ◽  
Nonminimal Coupling ◽  
Field Equations ◽  
Fermionic Field ◽  
Minimal Coupling ◽  
Constant Type

From a variational action with nonminimal coupling with a scalar field and classical scalar and fermionic interaction, cosmological field equations can be obtained. Imposing a Friedmann–Lemaître–Robertson–Walker (FLRW) metric, the equations lead directly to a cosmological model consisting of two interacting fluids, where the scalar field fluid is interpreted as dark energy and the fermionic field fluid is interpreted as dark matter. Several cases were studied analytically and numerically. An important feature of the non-minimal coupling is that it allows crossing the barrier from a quintessence to phantom behavior. The insensitivity of the solutions to one of the parameters of the model permits it to find an almost analytical solution for the cosmological constant type of universe.

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 PARAMETRIC NONHOLONOMIC FRAME TRANSFORMS AND EXACT SOLUTIONS IN GRAVITY

2007 ◽  
Vol 04 (08) ◽  
pp. 1285-1334 ◽  
Author(s):  
SERGIU I. VACARU
Keyword(s):  
Gravitational Field ◽  
Exact Solutions ◽  
General Scheme ◽  
Nonlinear Partial Differential Equations ◽  
Killing Vector ◽  
Field Equations ◽  
Finsler Spaces ◽  
Gravitational Field Equations ◽  
Pp Wave ◽  
Physical Consequences

A generalized geometric method is developed for constructing exact solutions of gravitational field equations in Einstein theory and generalizations. First, we apply the formalism of nonholonomic frame deformations (formally considered for nonholonomic manifolds and Finsler spaces) when the gravitational field equations transform into systems of nonlinear partial differential equations which can be integrated in general form. The new classes of solutions are defined by generic off-diagonal metrics depending on integration functions on one, two and three (or three and four) variables if we consider four (or five) dimensional spacetimes. Second, we use a general scheme when one (two) parameter families of exact solutions are defined by any source-free solutions of Einstein's equations with one (two) Killing vector field(s). A successive iteration procedure results in new classes of solutions characterized by an infinite number of parameters for a non-Abelian group involving arbitrary functions on one variable. Five classes of exact off-diagonal solutions are constructed in vacuum Einstein and in string gravity describing solitonic pp-wave interactions. We explore possible physical consequences of such solutions derived from primary Schwarzschild or pp-wave metrics.

Dynamical properties of scaling solutions in teleparallel dark energy cosmologies with nonminimal coupling

2017 ◽  
Vol 26 (09) ◽  
pp. 1750103 ◽  
Author(s):  
Mihai Marciu
Keyword(s):  
Dark Energy ◽  
Power Law ◽  
Scalar Fields ◽  
Teleparallel Gravity ◽  
Inverse Power ◽  
Coupling Coefficients ◽  
Potential Term ◽  
Inverse Power Law ◽  
The Stability ◽  
The Impact

The dynamical aspects of scaling solutions for the dark energy component in the theoretical framework of teleparallel gravity are considered, where dark energy is represented by a scalar field nonminimally coupled with the torsion and with a boundary term, where the boundary coupling term represents the divergence of the torsion vector. The behavior and stability of the scaling solutions are studied for scalar fields endowed with inverse power law potentials and with exponential potentials. It is shown that for scalar fields endowed with inverse power-law potentials, the stability conditions are not affected by the coupling coefficients. For the scalar fields endowed with exponential potentials, two cases are studied: at first, we have considered an infinitesimal deviation from the scaling solution in the corresponding Klein–Gordon equation, and the impact of distinct coupling coefficients on the stability of the solution are analyzed. Secondly, the potential-free case is considered where the dominance of the coupling terms over the potential term is analyzed, discussing the validity of the corresponding particular solution.

scholarly journals TELEPARALLEL ENERGY–MOMENTUM DISTRIBUTION OF LEWIS–PAPAPETROU SPACETIMES

2007 ◽  
Vol 22 (06) ◽  
pp. 425-433 ◽  
Author(s):  
M. SHARIF ◽  
M. JAMIL AMIR
Keyword(s):  
Energy Density ◽  
Momentum Distribution ◽  
Gravitational Effect ◽  
External Source ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Teleparallel Theory ◽  
Axisymmetric Solutions

In this paper, we find the energy–momentum distribution of stationary axisymmetric spacetimes in the context of teleparallel theory by using Möller prescription. The metric under consideration is the generalization of the Weyl metrics called the Lewis–Papapetrou metric. The class of stationary axisymmetric solutions of the Einstein field equations has been studied by Galtsov to include the gravitational effect of an external source. Such spacetimes are also astrophysically important as they describe the exterior of a body in equilibrium. The energy density turns out to be nonvanishing and well-defined and the momentum becomes constant except along θ-direction. It is interesting to mention that the results reduce to the already available results for the Weyl metrics when we take ω = 0.

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.

GRAVITATIONAL COLLAPSE OF THICK DOMAIN WALLS: AN ANALYTIC MODEL

1994 ◽  
Vol 09 (39) ◽  
pp. 3605-3609 ◽  
Author(s):  
ANZHONG WANG
Keyword(s):  
Domain Wall ◽  
Gravitational Collapse ◽  
Gravitational Radiation ◽  
Domain Walls ◽  
Analytic Model ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Pp Wave ◽  
Thick Domain Walls ◽  
Spacelike Infinity

An exact solution to the Einstein field equations is found, which represents the gravitational collapse of a thick domain wall. During the collapse, the wall emits gravitational radiation, which can be measured as a gravitational pp wave at the spacelike infinity. The time-reversed solution represents an expanding universe, in which a domain wall resides. It is shown explicitly that such a wall can be inflated away.

scholarly journals ON THE RELATION BETWEEN MASS AND CHARGE: A PURE GEOMETRIC APPROACH

2007 ◽  
Vol 04 (03) ◽  
pp. 373-388 ◽  
Author(s):  
M. I. WANAS
Keyword(s):  
Charged Particle ◽  
Riemannian Space ◽  
Central Body ◽  
Geometric Model ◽  
Geometric Approach ◽  
Massless Particle ◽  
Field Equations ◽  
Type Analysis ◽  
Gravitational Contribution ◽  
Better Than

A new solution to the field equations of the generalized field theory, constructed by Mikhail and Wanas in 1977, has been obtained. The geometric structure used, in the present application, is an absolute parallelism (AP)-space with spherical symmetry (type FIGI). The solution obtained represents a generalized field outside a charged massive central body. Two schemes have been used to get the physical meaning of the solution: The first is related to the metric of the Riemannian space associated with the AP-structure. The second is connected to a covariant scheme known as Type Analysis. It is shown that the dependence on both schemes for interpreting the results obtained, is better than the dependence on the metric of the Riemannian space associated with the AP-structure. In general, if we consider the solution obtained as representing a geometric model for an elementary charged particle, then the results of the present work can be summarized in the following points. (i) It is shown that the mass of the particle is made up of two contributions: the first is the gravitational contribution, and the second is the contribution due to the existence of charge. (ii) The model allows for the existence of a charged particle whose mass is completely electromagnetic in origin. (iii) The model prevents the existence of a charged massless particle. (iv) The electromagnetic contribution, to the mass, is independent of the sign of the electric charge. (v) It is shown that the mass of the electron (or a positron) is purely made of its charge.

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