Einstein-Cartan theory (ECT) is an extension of Einstein's general theory of relativity (GTR) that incorporates the concept of spin and torsion, in addition to curvature. In ECT, the fundamental building blocks of matter, such as elementary particles, possess intrinsic angular momentum or spin.
In ECT, the presence of torsion allows for a nonzero value of the "torsion tensor," which represents the twisting or shearing of spacetime. This additional geometric quantity can have implications for the behavior of matter and the structure of spacetime.
Regarding the issue of singularities, it's important to note that the existence or non-existence of singularities in any theory, including ECT, is still a subject of active research and debate among physicists. A singularity is a point in spacetime where the curvature becomes infinitely large, and the laws of physics break down.
While ECT has been explored as a possible avenue to address singularities, it does not necessarily eliminate them entirely. The presence or absence of singularities in a theory depends on various factors, including the specific conditions and assumptions used in the mathematical models.
It is true that the inclusion of spin and torsion in ECT provides additional mathematical tools to describe certain physical phenomena. However, it's worth noting that the standard formulation of general relativity, without torsion, has been remarkably successful in describing a wide range of astrophysical and cosmological phenomena. Moreover, observational evidence, such as the existence of black holes, suggests that singularities may indeed exist in our universe.
In summary, while ECT introduces interesting concepts and mathematical tools, the issue of singularities and their presence in the theory is still an open question. The advantages or disadvantages of ECT compared to GTR depend on specific contexts and the physical phenomena under consideration. Ongoing research and theoretical developments aim to deepen our understanding of these fundamental aspects of spacetime and gravity.