A primer on Carroll gravity

The ultra-relativistic limit of general relativity is Carroll gravity. In this article, we provide (i) a rigorous and thorough exposition of the geometric formalism of the 'magnetic' version of Carroll gravity, (ii) a presentation of this theory as a limit of general relativity in a geometrical, 'lightcone-narrowing' sense, and (iii) an exploration of some of the various conceptually interesting features of this version of Carroll gravity.
Comment: 29 pages