A primer on Carroll gravity

TL;DR

This paper thoroughly explains Carroll gravity, an ultra-relativistic limit of general relativity, focusing on its geometric formalism, derivation as a limit, and its unique conceptual features.

Contribution

It provides a rigorous geometric formalism of magnetic Carroll gravity and presents it as a limit of general relativity, highlighting its novel features.

Findings

Detailed geometric formalism of magnetic Carroll gravity

Derivation of Carroll gravity as a lightcone-narrowing limit of GR

Discussion of conceptual features of Carroll gravity

Abstract

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.