Non-Riemannian gravitational interactions

Tucker, Robin; Wang, Charles

doi:10.4064/-41-2-263-271

Cited by 10 publications

(17 citation statements)

References 17 publications

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“…Although there are good physical reasons for rejecting the pure Yang-Mills term in the Lagrangian by taking ρ 1 = 0, the general case is not more difficult for treatment, so we will consider the complete set of teleparallel models (2.2) with arbitrary values of parameters. The standard computations of the variation of a Lagrangian defined on a teleparallel manifold are rather complicated [23], [13]. It is because one needs to vary not only the coframe ϑ a itself, but also the the dual frame e a and even the Hodge dual operator * , that depends on the pseudo-orthonormal coframe implicitly.…”

Section: The Compact Form Of the Lagrangianmentioning

confidence: 99%

Energy–momentum current for coframe gravity

Itin

2001

Class. Quantum Grav.

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The obstruction for the existence of an energy momentum tensor for the gravitational field is connected with differential-geometric features of the Riemannian manifold. It has not to be valid for alternative geometrical structures. A teleparallel manifold is defined as a parallelizable differentiable 4D-manifold endowed with a class of smooth coframe fields related by global Lorentz, i.e., SO(1, 3) transformations. In this article a general free parametric class of teleparallel models is considered. It includes a 1-parameter subclass of viable models with the Schwarzschild coframe solution.A new form of the coframe field equation is derived from the general teleparallel Lagrangian by introducing the notion of a 3-parameter conjugate field strength F a . The field equation turns out to have a form completely similar to the Maxwell field equation d * F a = T a . By applying the Noether procedure, the source 3-form T a is shown to be connected with the diffeomorphism invariance of the Lagrangian. Thus the source T a of the coframe field is interpreted as the total conserved energy-momentum current. The energy-momentum tensor for coframe is defined. The total energymomentum current of a system of a coframe and a material fields is conserved. Thus a redistribution of the energy-momentum current between a material and a coframe (gravity) fields is possible in principle, unlike as in the standard GR. For special values of parameters, when the GR is reinstated, the energy-momentum tensor gives up the invariant sense, i.e., becomes a pseudo-tensor. Thus even a smallparametric change of GR turns it into a well defined Lagrangian theory.

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Section: The Compact Form Of the Lagrangianmentioning

confidence: 99%

Energy–momentum current for coframe gravity

Itin

2001

Class. Quantum Grav.

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“…Similar solutions have been found by Tucker and Wang, see [34] and [35]. The geometrical ingredients of MAG are the curvature two-form R α β = 1 2 R ijα β dx i ∧ dx j , and, as post-Riemannian structures, the nonmetricity one-form Q αβ = Q iαβ dx i and the torsion two-form T α = 1 2 T ij α dx i ∧ dx j .…”

Section: An Electric Charge In Einstein-dilation-shear Gravitymentioning

confidence: 50%

Maxwell's theory on a post-Riemannian spacetime and the equivalence principle

Puntigam

Lämmerzahl

Hehl

1997

Class. Quantum Grav.

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The form of Maxwell's theory is well known in the framework of general relativity, a fact that is related to the applicability of the principle of equivalence to electromagnetic phenomena. We pose the question whether this form changes if torsion and/or nonmetricity fields are allowed for in spacetime. Starting from the conservation laws of electric charge and magnetic flux, we recognize that the Maxwell equations themselves remain the same, but the constitutive law must depend on the metric and, additionally, may depend on quantities related to torsion and/or nonmetricity. We illustrate our results by putting an electric charge on top of a spherically symmetric exact solution of the metric-affine gauge theory of gravity (comprising torsion and nonmetricity). All this is compared to the recent results of Vandyck. file vandyck8.tex, 1997-02-11, Classical and Quantum Gravity, to be published (1997)

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“…Recently a different approach has been proposed [22][23][24] based on the metric g and the connection ∇ as independent variables. Instead of working with the group GL(4, R) (the general linear group), they rely on the definition of torsion and non-metricity in terms of g and ∇.…”

Section: Chapter 1 1 Introductionmentioning

confidence: 99%

My Life and Mathematics

Lancaster¹

2002

Linear Operators and Matrices

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I wish to thank in the first place my friend Emanuele Costa now at Edinburgh University with whom I shared most of my experience in Lancaster, he was not only a friend but also a guide especially during the difficult moments of my permanence in Lancaster. The interaction with many colleagues was invaluable first of all Dr. Charles Wang for teaching me many things about computer usage; his confidence in the frame independent approach to differential geometry was always inspiring for me.Thanks to some of my friends especially for the last period of my stay in

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Non-Riemannian gravitational interactions

Cited by 10 publications

References 17 publications

Energy–momentum current for coframe gravity

Energy–momentum current for coframe gravity

Maxwell's theory on a post-Riemannian spacetime and the equivalence principle

My Life and Mathematics

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