The geometry of the SL 2, C gauge formulation of general relativity

TLDR: In this paper, the formulation of the general theory of relativity as an SL2,C gauge theory is considered, and the spinor approach is compared with other approaches to the problem of formulating Einstein's theory as a gauge theory.

Abstract: The formulation of Einstein’s general theory of relativity as anSL2,C gauge theory is considered. Use is made of the language of fibre bundles and general arguments are put forward in favour of theSL2,C approach to problems connected with the study of the space-time structure. The possibility of deriving the dynamics of the theory from a Yang-Mills-type Lagrangian density is discussed. Finally, the spinor approach is compared with other approaches to the problem of formulating Einstein’s theory as a gauge theory.