On Hypermomentum in General Relativity I. The Notion of Hypermomentum

Hehl, Friedrich W.; Kerlick, G. David; Heyde, Paul von der

doi:10.1515/zna-1976-0201

Cited by 91 publications

(108 citation statements)

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“…As In two other articles, we shall present this physical idea in more detail (4). In particular, we shall show that the band-spinor description fits well into a recent generalization of general relativity, the metric-affine theory (5,6). This can be regarded as a GA(4,R) gauge, in which the vierbein is coupled minimally to the energy-momentum tensor, and the affine connection is similarly coupled to the intrinsic hypermomentum tensor whose components are the spin, dilation, and shear currents.…”

Section: Introductionmentioning

confidence: 69%

Gravitational interaction of hadrons: Band-spinor representations of GL(n,R)

Ne’eman

1977

Proc. Natl. Acad. Sci. U.S.A.

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We demonstrate the existence of double-valued linear (infinite) spinorial representations of the group of general coordinate transformations. We discuss the topology of the group of general coordinate transformations and its subgroups GA(nR), GL(nR) SL4nr) for n = 2,3,4, and the existence of a double covering. We present the construction of band-spinor representations of GLtnR) in terms of Harish-Chandra modules.It is suggested that hadrons interact with gravitation as band-spinors of that type. In the metric-affine extension of general relativity, the hadron intrinsic hypermomentum is minimally coupled to the connection, in addition to the coupling of the energy momentum tensor to the vierbeins. The relativistic conservation of intrinsic hypermomentum fits the observed regularities of hadrons: SU(6) (-spin independence), scaling, and complex-J trajectories. The latter correspond to volumepreserving deformations (confinement?) exciting rotational ands.

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Section: Introductionmentioning

confidence: 69%

Gravitational interaction of hadrons: Band-spinor representations of GL(n,R)

Ne’eman

1977

Proc. Natl. Acad. Sci. U.S.A.

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“…On the other hand, much work has also been done on alternative theories of gravitation [50]. It is by now well-known that when we describe gravity as the gauge theory of the Poincaré group, this naturally leads to theories with torsion [4][5][6][7]. The basic ideas can be summarized as follows [7,[51][52].…”

Section: Singularities For Theories With Torsionmentioning

confidence: 99%

“…The Poincaré group deserves special consideration because it corresponds to an external symmetry, it yields momentum and angular momentum conservation, and its translational part can be seen as carrying matter through space-time [6].…”

Section: Singularities For Theories With Torsionmentioning

confidence: 99%

“…This choice of arguments is motivated by the second part of our paper, where the singularity theory in cosmology for space-times with torsion is studied. In fact the Poincaré group can be seen as the subgroup of the BMS group which maps good cuts into good cuts, and it is also known that the gauge theory of the Poincaré group leads to theories with torsion [4][5][6][7]. Thus it appears important to clarify these properties.…”

Section: Introductionmentioning

confidence: 99%

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Mathematical Structures of Space-Time

Esposito

1992

Fortschr. Phys.

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Abstract. At first we introduce the space-time manifold and we compare some aspects of Riemannian and Lorentzian geometry such as the distance function and the relations between topology and curvature. We then define spinor structures in general relativity, and the conditions for their existence are discussed. The causality conditions are studied through an analysis of strong causality, stable causality and global hyperbolicity. In looking at the asymptotic structure of space-time, we focus on the asymptotic symmetry group of Bondi, Metzner and Sachs, and the b-boundary construction of Schmidt. The Hamiltonian structure of space-time is also analyzed, with emphasis on Ashtekar's spinorial variables.Finally, the question of a rigorous theory of singularities in space-times with torsion is addressed, describing in detail recent work by the author. We define geodesics as curves 1 Mathematical Structures of Space-Time whose tangent vector moves by parallel transport. This is different from what other authors do, because their definition of geodesics only involves the Christoffel symbols, though studying theories with torsion. We then prove how to extend Hawking's singularity theorem without causality assumptions to the space-time of the ECSK theory. This is achieved studying the generalized Raychaudhuri equation in the ECSK theory, the conditions for the existence of conjugate points and properties of maximal timelike geodesics. Our result can also be interpreted as a no-singularity theorem if the torsion tensor does not obey some additional conditions. Namely, it seems that the occurrence of singularities in closed cosmological models based on the ECSK theory is less generic than in general relativity.Our work should be compared with important previous papers. There are some relevant differences, because we rely on a different definition of geodesics, we keep the field equations of the ECSK theory in their original form rather than casting them in a form similar to general relativity with a modified energy-momentum tensor, and we emphasize the role played by the full extrinsic curvature tensor and by the variation formulae. * Fortschritte der Physik, 40, 1-30 (1992). 2Mathematical Structures of Space-Time

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“…31. It has the decomposition, where S αβ is the spin tensor, J is the dilatonic charge andĴ (αβ) is the intrinsic proper hypermomentum (shear) tensor.…”

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confidence: 99%