Einstein-Cartan theory as a theory of defects in space-time

Details Einstein-Cartan theory as a theory of defects in space-time Einstein-Cartan theory as a theory of defects in space-time

2003-06-07

arxiv.org/abs/gr-qc/0306029v2

Am.J.Phys. 71 (2003) 1303-1313

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

18 pages, 7 EPS figures, RevTeX4, to appear in the American Journal of Physics, revised version with typos corrected

Scientific paper

10.1119/1.1596176

The Einstein-Cartan theory of gravitation and the classical theory of defects in an elastic medium are presented and compared. The former is an extension of general relativity and refers to four-dimensional space-time, while we introduce the latter as a description of the equilibrium state of a three-dimensional continuum. Despite these important differences, an analogy is built on their common geometrical foundations, and it is shown that a space-time with curvature and torsion can be considered as a state of a four-dimensional continuum containing defects. This formal analogy is useful for illustrating the geometrical concept of torsion by applying it to concrete physical problems. Moreover, the presentation of these theories using a common geometrical basis allows a deeper understanding of their foundations.

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