General relativity with spin and torsion and its deviations from Einstein's theory

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

doi:10.1103/physrevd.10.1066

Cited by 200 publications

(289 citation statements)

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“…Accordingly, the singular big bang is replaced by a nonsingular big bounce from a contracting universe [14]. This result agrees with Hawking-Penrose singularity theorems because the contribution from torsion violates energy conditions at high densities [9]. Interestingly, loop quantum gravity also predicts a cosmic bounce [15].…”

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confidence: 75%

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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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confidence: 75%

“…Even if the spin orientation of particles is random, the macroscopic spacetime average of terms that are quadratic in the spin tensor does not vanish. In this case, the Einstein equations give [9,10] …”

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confidence: 99%

Cosmological consequences of gravity with spin and torsion

Popławski¹

2013

Astronomical Review

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“…It is shown that the torsion effect in the Einstein-Cartan (EC) theory, which is the simplest model of the gauge theory of gravity, may avert the initial singularity of the homogeneous but anisotropic universe [11], where the matter fields are described by a spin fluid [12]. It is also shown that EC theory may avert the big-bang singularity of the Robertson-Walker (RW) universe [13,14], where the matter fields are represented by another spin fluid [15,16]. In these works [13,14], an averaging procedure [15] is used such that the torsion field is equal to zero but the torsion effect does not vanish.…”

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confidence: 99%

R+S2 theories of gravity without big-bang singularity

2015

Annals of Physics

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The R + S 2 theories of gravity, where S 2 denotes the quadratic torsion terms, are analyzed under three cases. In the first two cases, the matter fields are described by two different spin fluids which are not homogeneous and isotropic. In the third case, a homogeneous and isotropic torsion field is used. It is found that under all the three cases, the R+S 2 theories may avert the big-bang singularity of the RobertsonWalker universe, with three corresponding constraints on the parameters.

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“…The work of S. Vacaru is supported by a NATO/Portugal fellowship at CENTRA, Instituto Superior Tecnico, Lisbon. The author is grateful to R. Ablamowicz, John Ryan, and B. Fauser for collaboration and support of his participation at "The 6th International Conference on Clifford Algebras," Cookeville, Tennessee, USA (May, [20][21][22][23][24][25] 2002). He would like to thank J. P. S. Lemos, R. Miron, M. Anastasiei, and P. Stavrinos for hospitality and support.…”

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“…Various types of Finsler-like structures can be parametrized by generic off-diagonal metrics, which cannot be diagonalized by coordinate transforms but only by anholonomic maps with associated nonlinear connection (in brief, N-connection). Such structures may be defined as exact solutions of gravitational field equations in the Einstein gravity and its generalizations [75,79,80,94,95,96,97,98,99,100,102,103,104,105,109,110,111], for instance, in the metric-affine [19,23,56] Riemann-Cartan gravity [24,25]. Finsler-like configurations are considered in locally anisotropic thermodynamics, kinetics, related stochastic processes [85,96,107,108], and (super-) string theory [84,87,90,91,92].…”

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confidence: 99%

Nonlinear connections and spinor geometry

Vacaru¹,

Vicol

2004

International Journal of Mathematics and Mathematical Sciences

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We present an introduction to the geometry of higher-order vector and covector bundles (including higher-order generalizations of the Finsler geometry and Kaluza-Klein gravity) and review the basic results on Clifford and spinor structures on spaces with generic local anisotropy modeled by anholonomic frames with associated nonlinear connection structures. We emphasize strong arguments for application of Finsler-like geometries in modern string and gravity theory, noncommutative geometry and noncommutative field theory, and gravity.2000 Mathematics Subject Classification: 15A66, 58B20, 53C60, 83C60, 83E15.1. Introduction. Nowadays, interest has been established in non-Riemannian geometries derived in the low-energy string theory [18,64,65], noncommutative geometry [1,3,8,12,15,22,32,34,53,55,67,109,111,112], and quantum groups [33,35,36,37]. Various types of Finsler-like structures can be parametrized by generic off-diagonal metrics, which cannot be diagonalized by coordinate transforms but only by anholonomic maps with associated nonlinear connection (in brief, N-connection). Such structures may be defined as exact solutions of gravitational field equations in the Einstein gravity and its generalizations [75,79,80,94,95,96,97,98,99,100,102,103,104,105,109,110,111], for instance, in the metric-affine [19,23,56] Riemann-Cartan gravity [24,25]. Finsler-like configurations are considered in locally anisotropic thermodynamics, kinetics, related stochastic processes [85,96,107,108], and (super-) string theory [84,87,90,91,92].The following natural step in these lines is to elucidate the theory of spinors in effectively derived Finsler geometries and to relate this formalism of Clifford structures to noncommutative Finsler geometry. It should be noted that the rigorous definition of spinors for Finsler spaces and generalizations was not a trivial task because (on such spaces) there are no defined even local groups of automorphisms. The problem was solved in [82,83,88,89,93] by adapting the geometric constructions with respect to anholonomic frames with associated N-connection structure. The aim of this work is to outline the geometry of generalized Finsler spinors in a form more oriented to applications in modern mathematical physics.We start with some historical remarks: the spinors studied by mathematicians and physicists are connected with the general theory of Clifford spaces introduced in 1876 [14]. The theory of spinors and Clifford algebras play a major role in contemporary physics and mathematics. The spinors were discovered by Èlie Cartan in 1913 in 1190 S. I. VACARU AND N. A. VICOL mathematical form in his researches on representation group theory [10,11]; he showed that spinors furnish a linear representation of the groups of rotations of a space of arbitrary dimensions. The physicists Pauli [60] and Dirac [20] (in 1927, resp., for the three-dimensional and four-dimensional space-times) introduced spinors for the representation of the wave functions. In general relativity theory spinors and the Dirac equat...

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General relativity with spin and torsion and its deviations from Einstein's theory

Cited by 200 publications

References 9 publications

Cosmological consequences of gravity with spin and torsion

Cosmological consequences of gravity with spin and torsion

R+S2 theories of gravity without big-bang singularity

Nonlinear connections and spinor geometry

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