Fluids on null hypersurfaces and Carrollian hydrodynamics

Abstract

We study intrinsic ideal fluids on null hypersurfaces and their realisations by causal fluids living in the ambient spacetime. An embedded null hypersurface is equipped with an induced Carrollian structure with a temporal Weyl symmetry inherited from rescalings of the null generator, and we develop the corresponding null submanifold and variational calculus. The intrinsic fluid phases are classified according to their realisation of Carroll boosts and temporal Weyl symmetry. If we demand that an ambient fluid be confined to a null hypersurface, the ambient fluid velocity must be null, which realises an intrinsic zero-temperature Carrollian phase with unbroken Carroll boosts. In general, timelike or null ambient fluids will cross a null hypersurface and lead to an open Carrollian system. On a null foliation, the sources correspond to transport between null leaves. We then show that there exists a decoupling limit of a timelike ambient fluid which gives rise to an autonomous Carrollian fluid with spontaneously broken Carroll boosts and no source terms. This decoupling limit corresponds to an infinite boost while keeping the enthalpy finite and nonzero, which leads to a divergent ambient energy-momentum tensor. Nevertheless, the induced Carrollian responses do not see the divergent term and remain finite, and an independent Carroll boost Goldstone emerges from a subleading component of the ambient fluid velocity in this limit.