The Einstein–yang–mills Equations From Bianchi Identities

Böhmer, Christian G.; Fabbri, Luca

doi:10.1142/s0217732307025807

Cited by 4 publications

(1 citation statement)

References 21 publications

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“…We will now impose a set of constraints on torsion and the Ricci rotation coefficients consistent with Cartan's structure equation [5] that relates torsion and connection coefficients. With a minimal modification of the standard general relativity in mind, we chose the set of constraints [6] so that the torsion components tangential to the 4D hypersurface vanish (see also [7]), while leaving non-vanishing torsion components completely determined in terms of the metric components of the 5D space-time. In the absence of torsion, the metric compatibility condition serves to evaluate the connection coefficients (Christoffel symbols, eq.…”

Section: Arxiv:09044038v2 [Gr-qc] 2 Apr 2010mentioning

confidence: 99%

Kaluza–klein Theory With Torsion Confined to the Extra Dimension

Shankar

Wali

2010

Mod. Phys. Lett. A

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Here we consider a variant of the 5 dimensional Kaluza-Klein theory within the framework of Einstein-Cartan formalism that includes torsion. By imposing a set of constraints on torsion and Ricci rotation coefficients, we show that the torsion components are completely expressed in terms of the metric. Moreover, the Ricci tensor in 5D corresponds exactly to what one would obtain from torsion-free general relativity on a 4D hypersurface. The contributions of the scalar and vector fields of the standard K-K theory to the Ricci tensor and the affine connections are completely nullified by the contributions from torsion. As a consequence, geodesic motions do not distinguish the torsion free 4D space-time from a hypersurface of 5D space-time with torsion satisfying the constraints. Since torsion is not an independent dynamical variable in this formalism, the modified Einstein equations are different from those in the general Einstein-Cartan theory. This leads to important cosmological consequences such as the emergence of cosmic acceleration.In any attempt to link fundamental matter fields with intrinsic spin to gravity, it becomes necessary to extend the Riemannian space-time to include torsion, defined to be the antisymmetric part of affine connection. The resulting theory of gravity, known as the Einstein-Cartan theory[1] treats the metric and torsion as two independent geometrical characteristics of space-time [2].Historically, beginning with the Kaluza-Klein (KK) theory, there has been a great interest in introducing extra dimensions of space-time to unify gravity with elementary particle interactions. In the KK theory, the scalar and vector fields, which are the extra dimensional components of the metric tensor contribute to the affine connection and the Ricci tensor and hence modify their values from the corresponding values in 4D space-time [3]. The contribution of these fields to the Einstein tensor are normally interpreted as gravity induced matter.In this work, we incorporate torsion into 5D KK theory [4]. The inclusion of torsion introduces free parameters in the affine connection and the Ricci tensor in addition to the contributions from extra dimensional metric components that occur in the torsion free KK theory. In this paper we impose a minimal set of conditions so as to restrict torsion to purely extra dimensional components and determine all its components in terms of the metric. Interestingly, the imposed conditions lead to a complete cancellation between the modifications induced by the extra dimensional metric components and the contributions from the torsion. Thus the Ricci tensor in 5D space-time in the resulting formalism is exactly the Ricci tensor in a torsion free 4D space-time. In the second part of the paper, we apply the action principle to derive the equations of motion of this formalism. The modified Einstein equations thus derived are finally applied to Robertson-Walker cosmology that leads to a novel expansion history for the universe (see figure 1).To describe the constraints to be i...

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Section: Arxiv:09044038v2 [Gr-qc] 2 Apr 2010mentioning

confidence: 99%

Kaluza–klein Theory With Torsion Confined to the Extra Dimension

Shankar

Wali

2010

Mod. Phys. Lett. A

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The torsion cosmology in Kaluza–Klein theory

Chen¹,

Jing²

2009

J. Cosmol. Astropart. Phys.

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We have studied the torsion cosmology model in Kaluza-Klein theory. We considered two simple models in which the torsion vectors are Aµ = (α, 0, 0, 0) and Aµ = a(t) 2 (0, β, β, β), respectively. For the first model, the accelerating expansion of the Universe can be not explained without dark energy which is similar to that in the standard cosmology. But for the second model, we find that without dark energy the effect of torsion can give rise to the accelerating expansion of the universe and the alleviation of the well-known age problem of the three old objects for appropriated value of the model parameter β. These outstanding features of the second torsion cosmology model have been supported by the Type Ia supernovae (SNIa) data.

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Torsion in extra-dimensions

Wali

2010

J. Phys.: Conf. Ser.

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The Einstein–yang–mills Equations From Bianchi Identities

Cited by 4 publications

References 21 publications

Kaluza–klein Theory With Torsion Confined to the Extra Dimension

Kaluza–klein Theory With Torsion Confined to the Extra Dimension

The torsion cosmology in Kaluza–Klein theory

Torsion in extra-dimensions

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