Problems with metric-teleparallel theories of gravitation

Kopczyński, Wojciech

doi:10.1088/0305-4470/15/2/020

Cited by 144 publications

(146 citation statements)

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“…However, it was immediately noticed that most of these solutions involve free functions which means that the torsion configurations are not determined unambiguously by the physical sources. This observation had stirred a confusion among the gravitational community [33,16,25,37]: indeed, how can (at least part of) the torsion be nondynamical and hence arbitrary when one "apparently" can measure the torsion with the help of the particles with spin? So (citing the title of the paper [16]), "can Poincaré gauge theory be saved?…”

Section: Algebraic Conditions On Torsionmentioning

confidence: 99%

Poincaré Gauge Gravity: Selected Topics

Obukhov

2006

Int. J. Geom. Methods Mod. Phys.

155

200

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In the gauge theory of gravity based on the Poincaré group (the semidirect product of the Lorentz group and the spacetime translations) the mass (energy-momentum) and the spin are treated on an equal footing as the sources of the gravitational field. The corresponding spacetime manifold carries the Riemann-Cartan geometric structure with the nontrivial curvature and torsion. We describe some aspects of the classical Poincaré gauge theory of gravity. Namely, the Lagrange-Noether formalism is presented in full generality, and the family of quadratic (in the curvature and the torsion) models is analyzed in detail. We discuss the special case of the spinless matter and demonstrate that Einstein's theory arises as a degenerate model in the class of the quadratic Poincaré theories. Another central point is the overview of the so-called double duality method for constructing of the exact solutions of the classical field equations.

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Section: Algebraic Conditions On Torsionmentioning

confidence: 99%

Poincaré Gauge Gravity: Selected Topics

Obukhov

2006

Int. J. Geom. Methods Mod. Phys.

155

200

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“…Let us recall here that the covariantization of the Dirac equation requires vielbeins. Moreover, tetrads appear naturally in the geometric framework as translational gauge fields, providing the socalled teleparallel formulation of relativity theory [5][6][7][8][9][10]. Because eq.…”

Section: Torsion Lagrangians and Coupled Particle-torsion Field Systemsmentioning

confidence: 99%

“…The fields B a and E a k plays the role of the magnetic and electric fields, respectively, with the internal O(2) index a describing the d = 2 nonrelativistic rotation group 9 .…”

Section: Torsion Lagrangians and Coupled Particle-torsion Field Systemsmentioning

confidence: 99%

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From Gauging Nonrelativistic Translations to N-Body Dynamics

Lukierski

Stichel²,

Zakrzewski

2001

Annals of Physics

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We consider the gauging of space translations with time-dependent gauge functions. Using fixed time gauge of relativistic theory, we consider the gaugeinvariant model describing the motion of nonrelativistic particles. When we use gauge-invariant nonrelativistic velocities as independent variables the translation gauge fields enter the equations through a d × (d + 1) matrix of vielbein fields and their Abelian field strengths, which can be identified with the torsion tensors of teleparallel formulation of relativity theory. We consider the planar case (d = 2) in some detail, with the assumption that the action for the dreibein fields is given by the translational Chern-Simons term. We fix the asymptotic transformations in such a way that the space part of the metric becomes asymptotically Euclidean. The residual symmetries are (local in * e-mail: lukier@ift.uni.wroc.pl † email: pstichel@gmx.de ‡ e-mail: W.J.Zakrzewski@durham.ac.uk 1 time) translations and rigid rotations. We describe the effective interaction of the d = 2 N -particle problem and discuss its classical solution for N = 2. The phase space Hamiltonian H describing two-body interactions satisfies a nonlinear equation H = H( x, p; H) which implies, after quantization, a nonstandard form of the Schrödinger equation with energy dependent fractional angular momentum eigenvalues. Quantum solutions of the two-body problem are discussed. The bound states with discrete energy levels correspond to a confined classical motion (for the planar distance between two particles r ≤ r 0 ) and the scattering states with continuum energy correspond to the classical motion for r > r 0 . We extend our considerations by introducing an external constant magnetic field and, for N = 2, provide the classical and quantum solutions in the confined and unconfined regimes.

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“…The tetrad theory of gravitation based on the geometry of absolute parallelism [5][6][7][8][9][10][11][12][13][14] can be considered as the closest alternative to general relativity, and it has a number of attractive features both from the geometrical and physical viewpoints. Absolute parallelism is naturally formulated by gauging space-time translations and underlain by the Weitzenböck geometry, which is characterized by the metricity condition and by the vanishing of the curvature tensor (constructed from the connection of the Weitzenböck geometry).…”

Section: Introductionmentioning

confidence: 99%