scholarly journals Energy-momentum of the Friedmann models in General Relativity and the teleparallel theory of gravity

2008 ◽  
Vol 86 (11) ◽  
pp. 1297-1302 ◽  
Author(s):  
M Sharif ◽  
M Jamil Amir
Keyword(s):  
General Relativity ◽  
Energy Density ◽  
Spherical Shell ◽  
Momentum Density ◽  
Friedmann Universe ◽  
Coupling Constant ◽  
Dimensionless Coupling ◽  
Teleparallel Theory ◽  
Theory Of Gravity ◽  
Dimensionless Coupling Constant

This paper is devoted to the evaluation of the energy-momentum density components for the Friedmann models. For this purpose, we have used Møller’s pseudotensor prescription in General Relativity and a certain energy-momentum density developed from Møller’s teleparallel formulation. We show that the energy density of the closed Friedmann universe vanishes on the spherical shell at the radius ρ = 2[Formula: see text]. This coincides with the earlier results available in the literature. We also discuss the energy of the flat and open models. A comparison shows a partial consistency between Møller’s pseudotensor for General Relativity and teleparallel theory. Further, we show that the results are independent of the free dimensionless coupling constant of the teleparallel gravity.PACS No.: 04.20.–q

scholarly journals TELEPARALLEL ENERGY–MOMENTUM DISTRIBUTION OF STATIC AXIALLY SYMMETRIC SPACETIMES

2008 ◽  
Vol 23 (37) ◽  
pp. 3167-3177 ◽  
Author(s):  
M. SHARIF ◽  
M. JAMIL AMIR
Keyword(s):  
General Relativity ◽  
Energy Density ◽  
Momentum Distribution ◽  
Coupling Constant ◽  
Axially Symmetric ◽  
Symmetric Spacetimes ◽  
Teleparallel Theory ◽  
Theory Of Gravity ◽  
Comparison Of The Results ◽  
Special Case

This paper is devoted to discuss the energy–momentum for static axially symmetric spacetimes in the framework of teleparallel theory of gravity. For this purpose, we use the teleparallel versions of Einstein, Landau–Lifshitz, Bergmann and Möller prescriptions. A comparison of the results shows that the energy density is different but the momentum turns out to be constant in each prescription. This is exactly similar to the results available in literature using the framework of general relativity. It is mentioned here that Möller energy–momentum distribution is independent of the coupling constant λ. Finally, we calculate energy–momentum distribution for the Curzon metric, a special case of the above-mentioned spacetime.

scholarly journals QUANTUM GRAVITY IN PLEBANSKI FORMULATION

2011 ◽  
Vol 26 (31) ◽  
pp. 2323-2333
Author(s):  
L. V. LAPERASHVILI
Keyword(s):  
General Relativity ◽  
Quantum Gravity ◽  
Gravitational Interaction ◽  
Graviton Mass ◽  
Coupling Constant ◽  
Independent Variables ◽  
Dimensionless Coupling ◽  
Theory Of Gravity ◽  
Dimensionless Coupling Constant ◽  
Nonperturbative Theory

We present a theory of four-dimensional quantum gravity with massive gravitons which may be essentially renormalizable. In Plebanski formulation of general relativity in which the tetrads, the connection and the curvature are all independent variables (and the usual relations among these quantities are valid only on-shell), we consider the nonperturbative theory of gravity with a nonzero background connection. We predict a tiny value of the graviton mass: mg≈1.5×10-42 GeV and extremely small dimensionless coupling constant of the perturbative gravitational interaction: g~10-60. We put forward the idea by Isimori56 on renormalizability of quantum gravity having multi-gravitons with masses m0, m1, …, mN-1.

scholarly journals Supergraph calculation of one-loop divergences in higher-derivative 6D SYM theory

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
I. L. Buchbinder ◽  
E. A. Ivanov ◽  
B. S. Merzlikin ◽  
K. V. Stepanyantz
Keyword(s):  
Effective Action ◽  
A Priori ◽  
Coupling Constant ◽  
Harmonic Superspace ◽  
Classical Action ◽  
Higher Derivative ◽  
Component Approach ◽  
Dimensionless Coupling ◽  
The One ◽  
Dimensionless Coupling Constant

Abstract We apply the harmonic superspace approach for calculating the divergent part of the one-loop effective action of renormalizable 6D, $$ \mathcal{N} $$ N = (1, 0) supersymmetric higher-derivative gauge theory with a dimensionless coupling constant. Our consideration uses the background superfield method allowing to carry out the analysis of the effective action in a manifestly gauge covariant and $$ \mathcal{N} $$ N = (1, 0) supersymmetric way. We exploit the regularization by dimensional reduction, in which the divergences are absorbed into a renormalization of the coupling constant. Having the expression for the one-loop divergences, we calculate the relevant β-function. Its sign is specified by the overall sign of the classical action which in higher-derivative theories is not fixed a priori. The result agrees with the earlier calculations in the component approach. The superfield calculation is simpler and provides possibilities for various generalizations.

scholarly journals f(T) gravity and energy distribution in Landau–Lifshitz prescription

2018 ◽  
Vol 27 (04) ◽  
pp. 1850039 ◽  
Author(s):  
M. G. Ganiou ◽  
M. J. S. Houndjo ◽  
J. Tossa
Keyword(s):  
General Relativity ◽  
Energy Density ◽  
Energy Distribution ◽  
Cosmic String ◽  
Mass Formula ◽  
Plane Symmetric ◽  
Symmetric Metrics ◽  
Teleparallel Theory ◽  
Momentum Complex ◽  
Theory View

We investigate in this paper the Landau–Lifshitz energy distribution in the framework of [Formula: see text] theory view as a modified version of Teleparallel theory. From some important Teleparallel theory results on the localization of energy, our investigations generalize the Landau–Lifshitz prescription from the computation of the energy–momentum complex to the framework of [Formula: see text] gravity as it is done in the modified versions of General Relativity. We compute the energy density in the first step for three plane-symmetric metrics in vacuum. We find for the second metric that the energy density vanishes independently of [Formula: see text] models. We find that the Teleparallel Landau–Lifshitz energy–momentum complex formulations for these metrics are different from those obtained in General Relativity for the same metrics. Second, the calculations are performed for the cosmic string spacetime metric. It results that the energy distribution depends on the mass [Formula: see text] and the radius [Formula: see text] of cosmic string and it is strongly affected by the parameter of the considered quadratic and cubic [Formula: see text] models. Our investigation with this metric induces interesting results susceptible to be tested with some astrophysics hypothesis.

scholarly journals Dynamics and the emergence of geometry in an information mesh

2020 ◽  
Vol 80 (8) ◽  
Author(s):  
Philip Tee
Keyword(s):  
Ground State ◽  
Quantum Particle ◽  
Coupling Constants ◽  
Coupling Constant ◽  
Graph Properties ◽  
Graph Theoretical Approach ◽  
Dimensionless Coupling ◽  
Dimensionless Coupling Constant ◽  
Ground State Geometry ◽  
The Continuum

Abstract The idea of a graph theoretical approach to modeling the emergence of a quantized geometry and consequently spacetime, has been proposed previously, but not well studied. In most approaches the focus has been upon how to generate a spacetime that possesses properties that would be desirable at the continuum limit, and the question of how to model matter and its dynamics has not been directly addressed. Recent advances in network science have yielded new approaches to the mechanism by which spacetime can emerge as the ground state of a simple Hamiltonian, based upon a multi-dimensional Ising model with one dimensionless coupling constant. Extensions to this model have been proposed that improve the ground state geometry, but they require additional coupling constants. In this paper we conduct an extensive exploration of the graph properties of the ground states of these models, and a simplification requiring only one coupling constant. We demonstrate that the simplification is effective at producing an acceptable ground state. Moreover we propose a scheme for the inclusion of matter and dynamics as excitations above the ground state of the simplified Hamiltonian. Intriguingly, enforcing locality has the consequence of reproducing the free non-relativistic dynamics of a quantum particle.

Vacuum effects in a spatially homogeneous and isotropic cosmological background

1992 ◽  
Vol 70 (2-3) ◽  
pp. 143-147
Author(s):  
Victor M. Villalba ◽  
Umberto Percoco
Keyword(s):  
Separation Of Variables ◽  
Particle Creation ◽  
Coupling Constant ◽  
Positive Cosmological Constant ◽  
Dirac Equations ◽  
Klein Gordon ◽  
Dimensionless Coupling ◽  
Spatially Homogeneous ◽  
Dimensionless Coupling Constant ◽  
Vacuum Effects

In this article we obtain, by separation of variables, an exact solution to the Klein–Gordon and Dirac equations in a cosmological, spatially-closed, Robertson–Walker space-time with a positive cosmological constant Λ. The model is associated with a universe filled with radiation. We analyze the phenomenon of particle creation for different values of the dimensionless coupling constant ξ.

BLACK HOLES AND SOLITONS OF THE NONLINEAR ISOVECTOR MODEL

2006 ◽  
Vol 21 (21) ◽  
pp. 4343-4354 ◽  
Author(s):  
NEMATOLLAH RIAZI ◽  
HASSAN NIAD ◽  
SEYED HOSSEIN HENDI
Keyword(s):  
Strong Coupling ◽  
Asymptotic Form ◽  
Flat Space ◽  
Strong Coupling Regime ◽  
Spherically Symmetric ◽  
Coupling Constant ◽  
Curved Space ◽  
Dimensionless Coupling ◽  
Dimensionless Coupling Constant ◽  
Black Hole Solutions

We formulate the nonlinear isovector model in a curved background and calculate the spherically symmetric solutions for weak and strong coupling regimes. The question whether gravity has appreciable effects on the structure of solitons will be examined, in the framework of the calculated solutions, by comparing the flat-space and curved-space solutions. It turns out that in the strong coupling regime, gravity has essential effects on the solutions. It is also shown that the asymptotic form of the metric conforms with that of the charged Reissner–Nordstrom metric. The dimensionless coupling constant of the model has a limit, beyond which a horizon appears in the solutions, indicating the presence of black hole solutions.

scholarly journals Teleparallel version of the Levi–Civita vacuum solutions and their energy contents

2008 ◽  
Vol 86 (9) ◽  
pp. 1091-1096 ◽  
Author(s):  
M Sharif ◽  
M Jamil Amir
Keyword(s):  
General Relativity ◽  
Momentum Distribution ◽  
Radial Direction ◽  
Torsion Tensor ◽  
Axial Vector ◽  
Coupling Constant ◽  
Teleparallel Theory ◽  
Vacuum Solutions ◽  
Vector Part

In this paper, we find the teleparallel version of the Levi–Civita metric and obtain tetrad and the torsion fields. The tensor, vector, and the axial-vector parts of the torsion tensor are evaluated. It is found that the vector part lies along the radial direction only while the axial-vector vanishes everywhere because the metric is diagonal. Further, we use the teleparallel version of Moller, Einstein, Landau–Lifshitz, and Bergmann–Thomson prescriptions to find the energy-momentum distribution of this metric and compare the results with those already found in General Relativity (GR). It is worth mentioning here that momentum is constant in both of the theories for all the prescriptions. The energy in teleparallel theory is equal to the corresponding energy in GR only in the Moller prescription for the remaining prescriptions, the energy does not agree in both theories. We also conclude that Moller's energy-momentum distribution is independent of the coupling constant λ in the teleparallel theory.PACS Nos.: 04.20.–q, 04.20.Cv

scholarly journals TELEPARALLEL KILLING VECTORS OF THE EINSTEIN UNIVERSE

2008 ◽  
Vol 23 (13) ◽  
pp. 963-969 ◽  
Author(s):  
M. SHARIF ◽  
M. JAMIL AMIR
Keyword(s):  
General Relativity ◽  
Lie Derivative ◽  
Einstein Universe ◽  
Killing Vectors ◽  
Rank Tensor ◽  
Teleparallel Theory ◽  
Theory Of Gravity ◽  
Definition Of

In this paper we establish the definition of the Lie derivative of a second rank tensor in the context of teleparallel theory of gravity and also extend it for a general tensor of rank p + q. This definition is then used to find Killing vectors of the Einstein universe. It turns out that Killing vectors of the Einstein universe in the teleparallel theory are the same as in general relativity.

Comments on the Cosmological Constant Problem and How it Can be Solved

1997 ◽  
Vol 06 (05) ◽  
pp. 643-648 ◽  
Author(s):  
Paul S. Wesson
Keyword(s):  
General Relativity ◽  
Energy Density ◽  
Cosmological Constant ◽  
Dimensional Theory ◽  
Cosmological Constant Problem ◽  
Higher Dimensional ◽  
Theory Of Gravity

The problem of disparate estimates of the energy density of the vacuum can be solved, at least in principle, by reducing a higher-dimensional theory of gravity to general relativity and a local cosmological "constant."

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