Carrollian hydrodynamics from symmetries

Abstract

In this work, we revisit Carrollian hydrodynamics, a type of non-Lorentzian hydrodynamics which has recently gained increasing attentions due to its underlying connection with dynamics of spacetime near null boundaries, and we aim at exploring symmetries associated with conservation laws of Carrollian fluids. With an elaborate construction of Carroll geometries, we generalize the Randers-Papapetrou metric by incorporating the fluid velocity field and the sub-leading components of the metric into our considerations and we argue that these two additional fields are compulsory phase space variables in the derivation of Carrollian hydrodynamics from symmetries. We then present a new notion of symmetry, called the near-Carrollian diffeomorphism, and demonstrate that this symmetry consistently yields a complete set of Carrollian hydrodynamic equations. Furthermore, due to the presence of the new phase space fields, our results thus generalize those already presented in the previous literatures. Lastly, the Noether charges associated with the near-Carrollian diffeomorphism and their time evolutions are also discussed.

25 pages+appendices, 1 figure

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• Quantum Null Geometry and Gravity
• Heavy-ion collisions, Gubser flow, and Carroll hydrodynamics
• Renormalization of conformal infinity as a stretched horizon
• Carrollian Supersymmetry and SYK-like models
• Carrollian Yang-Mills Theory
• Fluid-gravity correspondence and causal first-order relativistic viscous hydrodynamics
• Migrating Carrollian particles on magnetized black hole horizons
• Radiation in Fluid/Gravity and the Flat Limit
• Quantization of Carrollian fermions
• Towards Quantizing Null p-branes: Light-Cone Gauge Analysis and Physical Hilbert Space
• Asymptotic Limit of Null Hypersurfaces
• One-loop partition function of gravity with leaky boundary conditions
• Supersymmetric Carroll Galileons in Three Dimensions
• Universal sectors of two-dimensional Carrollian CFTs
• Unique Carrollian manifolds emerging from Einstein spacetimes
• Sourced Carrollian Fluids Dual to Black Hole Horizons
• Rotating Carroll Black Holes: A No Go Theorem