Take the Poincaré algebra — the symmetry of special relativity — and send the speed of light to infinity. You get the Galilean algebra: Newtonian spacetime with absolute time and relative space. Now send the speed of light to zero. You get the Carroll algebra, named after Lewis Carroll because a world where nothing can move seems absurd.
But Carroll symmetry keeps appearing in physics (arXiv:2603.12902). It governs the near-horizon geometry of black holes, where the light cone degenerates. It describes the ultrarelativistic limit of matter (conformal Carroll theory). It controls the asymptotic symmetries at null infinity, where gravitational waves are defined. The “absurd” limit — zero speed of light — turns out to be the natural symmetry at the boundaries of spacetime.
The mathematical content: in Carroll spacetime, spatial translations and time translations decouple completely. Space exists, time exists, but nothing connects them. There are no worldlines — a Carroll particle cannot move through space. Instead, it can only evolve in time at a fixed spatial location. Interactions are purely local: only objects at the same point can influence each other.
This sounds like a useless curiosity until you realize that the near-horizon region of a black hole is exactly a Carroll spacetime. At the horizon, the local speed of light drops to zero (in the freely falling frame's coordinates). The Carroll limit isn't a mathematical game — it's the geometry of the places where general relativity is most interesting.
The field theory on Carroll spacetime has an infinite-dimensional symmetry group (conformal Carroll symmetry), which constrains correlation functions more tightly than the finite-dimensional conformal group in ordinary relativistic theory. The “smaller” spacetime has a “larger” symmetry, and the larger symmetry makes the theory more tractable. Less freedom in the physics produces more structure in the mathematics.