# Derivation of Einstein–Cartan theory from general relativity

@article{Petti2013DerivationOE, title={Derivation of Einstein–Cartan theory from general relativity}, author={Richard James Petti}, journal={International Journal of Geometric Methods in Modern Physics}, year={2013} }

This paper derives the elements of classical Einstein–Cartan theory (EC) from classical general relativity (GR) in two ways. (I) Derive discrete versions of torsion (translational holonomy) and the spin-torsion field equation of EC from one Kerr solution in GR. (II) Derive the field equations of EC as the continuum limit of a distribution of many Kerr masses in classical GR. The convergence computations employ “epsilon-delta” arguments, and are not as rigorous as convergence in Sobolev norm…

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## References

SHOWING 1-10 OF 62 REFERENCES

On the local geometry of rotating matter

- Physics
- 1986

This paper shows that general relativity and ordinary continuum models of matter imply the presence of Cartan torsion. The key concept is that torsion can be viewed as translational holonomy per unit…

Gauge Theory of Gravity and Spacetime

- Physics
- 2012

The advent of general relativity in 1915/1916 induced a paradigm shift: since then, the theory of gravity had to be seen in the context of the geometry of spacetime. An outgrowth of this new way of…

General Relativity with Spin and Torsion: Foundations and Prospects

- Physics
- 1976

A generalization of Einstein's gravitational theory is discussed in which the spin of matter as well as its mass plays a dynamical role. The spin of matter couples to a non-Riemannian structure in…

Lorentz Invariance and the Gravitational Field

- Physics
- 1961

An argument leading from the Lorentz invariance of the Lagrangian to the introduction of the gravitational field is presented. Utiyama's discussion is extended by considering the 10‐parameter group…

Nonsingular, big-bounce cosmology from spinor-torsion coupling

- Physics
- 2012

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…

Affine Defects and Gravitation

- Physics
- 2001

We argue that the structure general relativity (GR) as a theory of affine defects is deeper than the standard interpretation as a metric theory of gravitation. Einstein–Cartan theory (EC), with its…

On the energy tensor of spinning massive matter in classical field theory and general relativity

- Physics
- 1976

Gauge Theories Of Gravitation: A Reader With Commentaries

- Physics
- 2013

The Rise of Gauge Theory of Gravity Up to 1961: From Special to General Relativity Theory Analyzing General Relativity Theory A Fresh Start by Yang - Mills and Utiyama Poincare Gauge Theory: Einstein…