Gravitational Constant and Torsion

Mahato, Prasanta

doi:10.1142/s0217732302008460

Cited by 16 publications

(23 citation statements)

References 16 publications

(8 reference statements)

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“…The space time manifold now corresponds to the de Sitter space M 4,1 . In this framework SO(4, 1) Pontryagin density can be written as [23,29] …”

Section: Topological Densities and Gravity Lagrangianmentioning

confidence: 99%

“…Recently, it has been shown that [23], in U 4 space one can locally consider a particular term from this SO(4, 1) Pontryagin density as the gravitational Lagrangian [30], given by…”

Section: Topological Densities and Gravity Lagrangianmentioning

confidence: 99%

“…Recently a gravitational Lagrangian has been been proposed [23] where a Lorentz invariant part of the de Sitter Pontryagin density has been treated as the Einstein-Hilbert Lagrangian.…”

Section: Introductionmentioning

confidence: 99%

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de Sitter group and Einstein-Hilbert Lagrangian

Mahato¹

2004

Phys. Rev. D

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Axial vector torsion in the Einstein-Cartan space U 4 is considered here. By picking a particular term from the SO(4, 1) Pontryagin density and then modifying it in a SO(3, 1) invariant way, we get a Lagrangian density with Lagrange multipliers. Then considering torsion and torsion-less connection as independent fields, it has been found that κ and λ of Einstein-Hilbert Lagrangian, appear as integration constants in such a way that κ has been found to be linked with the topological Nieh-Yan density of U 4 space.

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“…The space time manifold now corresponds to the de Sitter space M 4,1 . In this framework SO(4, 1) Pontryagin density can be written as [23,29] …”

Section: Topological Densities and Gravity Lagrangianmentioning

confidence: 99%

“…Recently, it has been shown that [23], in U 4 space one can locally consider a particular term from this SO(4, 1) Pontryagin density as the gravitational Lagrangian [30], given by…”

Section: Topological Densities and Gravity Lagrangianmentioning

confidence: 99%

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de Sitter group and Einstein-Hilbert Lagrangian

Mahato¹

2004

Phys. Rev. D

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“…Thus de Sitter gauge theory comes up as the corrected Poincare gauge theory [5]. Recently a gravitational Lagrangian has been proposed [6], where a Lorentz invariant part of the de Sitter Pontryagin density has been treated as the Einstein-Hilbert Lagrangian. In this formalism the role of torsion in the underlying manifold is multiplicative rather than additive and the Lagrangian looks like torsion⊗curvature.…”

Section: Introductionmentioning

confidence: 99%

Torsion, Chern–simons Term and Diffeomorphism Invariance

Mahato¹,

Bhattacharya

2011

Mod. Phys. Lett. A

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In the torsion⊗curvature approach of gravity Chern-Simons modification has been considered here. It has been found that Chern-Simons contribution to the bianchi identity has become cancelled from that of the scalar field part. But "homogeneity and isotropy" consideration of present day cosmology is a consequence of the "strong equivalence principle" and vice-versa.1 It is to be noted here that in the presence of spinorial matter only the axial vector part of the torsion couples to the spinor field [8,9].

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“…† † The same connection with different gravitational dynamics has also been studied (See, e.g., Refs. [39][40][41][42][43][44][45][46][47][48][49][50] which are defined as:…”

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confidence: 99%

On torsion-free vacuum solutions of the model of de Sitter gauge theory of gravity (II)

Huang

2009

Front. Phys. China

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It is shown that all torsion-free vacuum solutions of the model of de Sitter (dS) gauge theory of gravity are the vacuum solutions of Einstein field equations with the same positive cosmological constant. Furthermore, for the gravitational theories with more general quadratic gravitational Lagrangian (F 2 + T 2 ), the torsion-free vacuum solutions are also the vacuum solutions of Einstein field equations.Keywords torsion-free vacuum solutions, model of de sitter gauge theory, gravity PACS numbers 04.20.Jb The astronomical observations show that our universe is probably an asymptotically de Sitter(dS) one [1][2][3][4][5][6]. This raises the interest on dS gauge theories of gravity. There is a model of dS gravity † , which was first proposed in the 1970s [7][8][9][10][11][12][13][14]. The dS gravity can be stimulated from dS invariant special relativity [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31] and the principle of localization -the full symmetry of the special relativity as well as the laws of dynamics are both localized [32-37] -and realized in terms of the dS connection on a kind of totally umbilical submanifolds (under the dS-Lorentz gauge) and Yang-Mills type action [7][8][9][10][11][12][32][33][34][35][36]. It has been shown [35,36] that the dS gravity may explain the accelerating expansion and supply a natural transit from decelerating expansion to accelerating expansion without the help of the introduction of matter fields in addition to dust. The different de Sitter spacetimes with nonzero torsion in the dS gravity have been presented in Ref.[38]. It has also been shown that all vacuum solutions of Einstein field equations with a cosmological constant are the vacuum solutions of the set of field equations without torsion [32][33][34]37]. In particular, Schwarzschild-dS and Kerr-dS metrics are two solutions. The purpose of the present letter is to show that all vacuum, torsion-free solutions in the dS gravity are the vacuum solutions of Einstein field equations with the same positive cosmological constant. Therefore, one may expect that the dS gravity may pass all solar-system-scale observations and experimental tests for general relativity (GR).The dS gauge theory of gravity is established based on the following consideration. The non-gravitational theory is de Sitter invariant special relativity. The theory of gravity should follow the principle of localization, which says that the full symmetry as well as the laws of dynamics are both localized, and the gravitational action takes Yang-Mills-type.A model of dS gauge theory of gravity has been constructed [7][8][9][10][11][12][13][14][32][33][34][35][36][37] in terms of the de Sitter connection in the dS-Lorentz frame, which reads † †where B AB μ = η BC B A Cμ . Its curvature is thenwhere e a bμν = e a μ e bν − e a ν e bμ , e aμ = η ab e b μ , F ab μν and T a μν are the curvature and torsion of the Lorentz connection † Hereafter, the model of dS gauge theory of gravity is called the dS gravity for short in this paper. † † The...

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Gravitational Constant and Torsion

Abstract: Riemann–Cartan space–time U4 is considered here. It has been shown that when we link topological Nieh–Yan density with the gravitational constant, we then obtain Einstein–Hilbert Lagrangian as a consequence.

Cited by 16 publications

References 16 publications

de Sitter group and Einstein-Hilbert Lagrangian

de Sitter group and Einstein-Hilbert Lagrangian

Torsion, Chern–simons Term and Diffeomorphism Invariance

On torsion-free vacuum solutions of the model of de Sitter gauge theory of gravity (II)

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