Einstein's theory admits interesting limits with different causal structures obtained by letting the speed of light go to infinity (Galilean or "non-relativistic" limit) or to zero (Carrollian, sometimes called "ultrarelativistic", limit). The Carroll limit turns out to be relevant near spacelike (cosmological) singularities, and particularly so when p-form gauge fields are coupled to gravity as in the context of extended supergravities. The resulting differential equations possess a remarkable interpretation in terms of infinite-dimensional Kac-Moody algebras. The talk will review various aspects of Carroll invariant theories, of the Belinski-Khalatnikov-Lifshitz analysis of spacelike singularities and of the related symmetries.
Laurent Freidel, Joshua Kirklin