As in the classical case from the torsion-free condition (i.e., (D4)) we immediately infer the symmetry of the Christoffel symbols of the Levi-Civita connection in the lower pair of indices.
Generalized pseudo-Riemannian geometry
Whether the extension due to the torsion ﬁeld has antisymmetry in two or three indices. • Whether the coupling constants corresponding to the different pseudo-tensorial extensions are the same or different.
Parity violation in four and higher dimensional spacetime with torsion
This can be interpreted as an indication that source of the torsion can be also the mass of the bodies that create the gravitational ﬁeld, not only the spin.
Schwarzschild solution on a space-time with torsion
The piece ◦ωa[bc] of the spin connection, antisymmetric in the last two indices as in (4), has the look of a torsion, but there is no torsion available: the only connection involved is the zerotorsion Levi-Civita connection.
Spin and Anholonomy in General Relativity
Gilbert Baumslag gave a counter example in that shows that not every subgroup of the generalized free product of two ﬁnitely generated torsion-free nilpotent groups is indicable.
On the residual solvability of generalized free products of finitely generated nilpotent groups
Higman proves that every ﬁnitely generated torsion-free nilpotent group is indicable and is therefore inﬁnite.
On the residual solvability of generalized free products of finitely generated nilpotent groups
The Matsumoto torsion Mj k l = Cj k l − 1 (n+1) P(j k l) Ij hk l can then be constructed using the above quantities together with an angular metric deﬁned by hj k = gj k − Fuj Fuk , where the subscripts again indicate differentiation.
Classical Lagrangians for Momentum Dependent Lorentz Violation
This could arguably be seen as one of the indications that torsion must be present in a fundamental theory of gravity, as discussed in .
The bimetric variational principle for General Relativity
Blayne Heckel ﬁnally identiﬁed the problem: the commercial computer-controlled micropositioning stage from which the torsion ﬁber was suspended had a scale factor error–it actually moved only ≈ 98% as far as it indicated.
Sub-mm tests of the gravitational inverse-square law
This result may be interpreted as an indication that, according to this approach, curvature and torsion might be equivalent ways of describing the gravitational ﬁeld, and consequently related with the same degrees of freedom of gravity .
General Relativity as a Genuine Connection Theory
The third column indicates the identiﬁcation as torsional shear modes on the basis of models that do not include crust-core coupling.
Neutron star oscillations and QPOs during magnetar flares
Estimates of the gravitational wave emission of crustal torsional shear vibrations indicate that the signals would be far too weak to be detected even by Advanced LIGO (Schumaker & Thorne, 1983).
Neutron star oscillations and QPOs during magnetar flares
The contorsion tensor is fully antisymmetric on its ﬁrst two indices, while the torsion tensor is fully antisymmetric on its last two indices.
Chern-Simons Modified General Relativity
Section 2 reviews some background on torsion indices and algebraic cobordism.
Algebraic cobordism of varieties with G-bundles
We emphasize that the proofs are relatively formal from Lemma 5.1.1, the properties of torsion indices, and the existence of enough characteristic classes.
Algebraic cobordism of varieties with G-bundles
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