The gauge theoretical underpinnings of general relativity

Abstract

The gauge theoretical formulation of general relativity is presented. We are only concerned with local intrinsic geometry, i.e. our space-time is an open subset of a four-dimensional real vector space. Then the gauge group is the set of differentiable maps from this open subset into the general linear group or into the Lorentz group or into its spin cover.

12 pages, 3 figures. Contribution to the Heraeus-Seminar "100 Years of Gauge Theory" organized by Silvia De Bianchi and Claus Kiefer, 30 July - 3 August 2018, Physikzentrum Bad Honnef. To appear in the proceedings "100 Years of Gauge Theory. Past, present and future perspectives" in the series `Fundamental Theories of Physics' (Springer)