TL;DR
This paper proposes that general relativity can be understood as a theory of affine defects, with Einstein-Cartan theory serving as a more fundamental framework, linking discrete affine defects to gravitation and quantum theory.
Contribution
It introduces a discrete affine interpretation of Einstein-Cartan theory, connecting affine defects to topological conservation laws and quantum foundations of gravity.
Findings
Affine defects offer a deeper understanding of GR.
Discrete affine interpretation yields topological conservation laws.
Quantum considerations support affine defects as the basis of gravitation.
Abstract
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 inhomogenous affine symmetry, should be the standard-bearer for GR-like theories. A discrete affine interpretation of EC (and gauge theory) yields topological definitions of momentum and spin (and Yang Mills current), and their conservation laws become discrete topological identities. Considerations from quantum theory provide evidence that discrete affine defects are the physical foundation for gravitation.
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