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

M. L. Ruggiero, A. Tartaglia
2003 American Journal of Physics  
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
more » ... ion 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.
doi:10.1119/1.1596176 fatcat:ktaolfospfgvtbnskqzxuu7lpu