Carroll Expansion of General Relativity

Understand

We study the small speed of light expansion of general relativity, utilizing the modern perspective on non-Lorentzian geometry.

• This is an expansion around the ultra-local Carroll limit, in which light cones close up.
• To this end, we first rewrite the Einstein-Hilbert action in pre-ultra-local variables, which is closely related to the 3+1 decomposition of general relativity.
• At leading order in the expansion, these pre-ultra-local variables yield Carroll geometry and the resulting action describes the electric Carroll limit of general relativity.