Nonlinear Spinor Equation and Asymmetric Connection in General Relativity

Hehl, Friedrich W.; Datta, Bithin

doi:10.1063/1.1665738

Cited by 234 publications

(244 citation statements)

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“…Varying L m with respect to the spinor adjoint conjugateψ gives the Dirac equation iγ k ψ ;k = mψ, which can be written as iγ k ψ :k = mψ − 3 8 κ(ψγ k γ 5 ψ)γ k γ 5 ψ and whose conjugate is −iψ :k γ k = mψ − 3 8 κ(ψγ k γ 5 ψ)ψγ k γ 5 [3,5]. Putting this equation in the energy-momentum tensor corresponding to the Dirac Lagrangian,…”

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confidence: 99%

Nonsingular, big-bounce cosmology from spinor-torsion coupling

2012

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The Einstein-Cartan-Sciama-Kibble theory of gravity removes the constraint of general relativity that the affine connection be symmetric by regarding its antisymmetric part, the torsion tensor, as a dynamical variable. The minimal coupling between the torsion tensor and Dirac spinors generates a spin-spin interaction which is significant in fermionic matter at extremely high densities. We show that such an interaction averts the unphysical big-bang singularity, replacing it with a cusp-like bounce at a finite minimum scale factor, before which the Universe was contracting. This scenario also explains why the present Universe at largest scales appears spatially flat, homogeneous and isotropic.

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confidence: 99%

Nonsingular, big-bounce cosmology from spinor-torsion coupling

2012

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“…Because of the Cartan equations (1), the torsion tensor is quadratic in spinor fields. Its substitution into the Dirac equation gives the cubic Hehl-Datta equation for ψ [5,6].…”

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confidence: 99%

“…The second term on the right of (4) corresponds to an effective axial-axial, four-fermion interaction [1,5],…”

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confidence: 99%

Cosmological consequences of gravity with spin and torsion

Popławski¹

2013

Astronomical Review

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We show that the Einstein-Cartan-Sciama-Kibble theory of gravity with torsion not only extends general relativity to account for the intrinsic spin of matter, but it may also eliminate major problems in gravitational physics and answer major questions in cosmology. These problems and questions include: the origin of the Universe, the existence of singularities in black holes, the nature of inflation and dark energy, the origin of the matter-antimatter asymmetry in the Universe, and the nature of dark matter.The big-bang cosmology, based on Einstein's general theory of relativity (GR), successfully describes primordial nucleosynthesis and predicts the cosmic microwave background radiation. It does not, however, address some fundamental questions. What is the origin of the rapid expansion of the Universe from an initial, extremely hot and dense state? What is the nature of dark energy? And what caused the observed asymmetry between matter and antimatter in the Universe? The validity of GR also breaks inside black holes and at the beginning of the big bang, where the matter is predicted to compress indefinitely to curvature singularities. The big-bang cosmology also requires an inflationary scenario with additional fields to explain why the present Universe appears spatially flat, homogeneous and isotropic. In this essay, we briefly describe how the solution to the above questions and problems may come from an old adaptation of GR, the Einstein-Cartan-Sciama-Kibble (ECSK) theory of gravity [1][2][3]. This classical theory naturally extends GR to account for the quantum-mechanical, intrinsic angular momentum (spin) of elementary particles that compose gravitating matter, causing spacetime to exhibit a geometric property called torsion.The ECKS gravity is based on the gravitational Lagrangian density proportional to the curvature scalar, as in GR. This theory, however, removes the GR restriction of the affine connection Γ k i j be symmetric. Instead, the antisymmetric part of the connection S k ij = Γ k [i j] (torsion tensor) is regarded as a dynamical variable like the metric tensor g ik . Varying the total action for the gravitational field and matter with respect to the metric gives the Einstein equations that relate the curvature to the dynamical energy-momentum tensor T ik = (2/ √ −g)δL/δg ik , where L is the matter Lagrangian density and g = det(g ik ) [4]. These equations can be written in a GR form as G ik = κ(T ik + U ik ), where the source is the modified energy-momentum tensor with an additional term U ik quadratic in the torsion tensor. G ik is the standard Einstein tensor and κ = 8πG/c 4 . These equations can also be written as R ik − R j j g ik /2 = κθ ik , where R ik (Γ) is the Ricci tensor of the connection and θ ik is the canonical energy-momentum tensor.Varying the total action with respect to the torsion gives the Cartan equations [1-3],

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“…Furthermore, the Dirac operator a a γ D ∇ = is unique for all spin connections a ∇ satisfying conditions (1) and (2).…”

Section: Theoremmentioning

confidence: 99%

“…To define bispinors, even in a Minkowski space-time, a reference tetrad or its equivalent (e.g., a normal coordinate basis) must first be defined at each point of the space-time [2] - [5], [15] - [17]. Note that the use of such reference tetrads has a long history, dating back to Weyl's 1929 paper [6].…”

Section: Introductionmentioning

confidence: 99%