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General Relativity as a (constrained) Yang-Mills's Theory and a Novel Gravity with Torsion

M. Botta Cantcheff
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Abstract

We show that General Relativity (GR) with cosmological constant may be formulated as a rather simple constrained SO(D-1,2) (or SO(D,1))-Yang-Mills (YM) theory. Furthermore, the spin connections of the Cartan-Einstein formulation for GR appear as solutions of a genuine SO(D-1,1)-YM. We also present a theory of gravity with torsion as the most natural extension of this result. The theory comes out to be strictly an YM-theory upon relaxation of a suitable constraint. This work sets out to enforce the close connection between YM theories and GR by means of a new construction.

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M. Botta Cantcheff. 2001-10-07. General Relativity as a (constrained) Yang-Mills's Theory and a Novel Gravity with Torsion. https://arxiv.org/abs/gr-qc/0010080

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