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.

Non-linear black hole dynamics and Carrollian fluids

“…Although this structure can be defined intrinsically for any given null surface (e.g. [24][25][26], it is perhaps easier to make the identification by comparing the near-horizon geometry (2.1) with the Randers-Papapetrou parameterization [27], given by…”

“…Also, from the full spacetime point of view, this stress energy tensor is obtained through a suitable projection with h ab . This projector is not unique but is invariant with respect of scalings, see [32]. Regardless, once a pair of null vectors {l, n}is defined a consistent decomposition is made, and employed to study a black hole's behavior and explore its dynamics from several angles as we do in this work.…”

“…A Carrollian fluid can be described as the c → 0 limit of a relativistic fluid [26,34]. Upon taking the limit, the fluid is described by a similar set of hydrodynamical variables: the energy density e, the pressure p, a pair of heat currents J A and π A , and a pair of dissipation tensors Σ AB and Π AB .…”

“…the stress energy tensor of a Carrollian fluid [26,32]. The main difference lies on the ambiguity in assigning contributions to pressure and the bulk viscosity ζ term of the dissipation.…”

Electric/magnetic Newton-Hooke and Carroll Jackiw-Teitelboim gravity

“…There has recently been a surge in interest in non-Lorentzian theories and their associated geometries. The reasons are several: their applications in condensed matter physics [2,3], non-relativistic holographic theories [4][5][6][7][8], Einstein gravity and black holes [9][10][11][12][13][14][15], and also in hydrodynamics [16][17][18].…”