Symplectic Analysis of Null Raychaudhuri

Working intrinsically on a null hypersurface, we first show that the Raychaudhuri constraint is the conservation law of a Carrollian stress tensor. After suitably dressing the diffeomorphisms with the internal boost symmetry, we derive the full kinematical Poisson bracket. The diffeomorphism boost charge turns out to be positive and monotonic in the dressing time. We then perform a perturbative analysis in the weak gravity regime, and show how the Raychaudhuri constraint can be interpreted as an equality of CFT stress tensors for the spin-0, spin-2, and matter systems. Finally, we observe that the perturbative spin-0 stress tensor and Poisson bracket behave exactly like a curved beta-gamma CFT.