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.

/pdf/carrollian-hydrodynamics-from-symmetries-3f7ochlr.pdf

Carrollian hydrodynamics from symmetries

In many areas of physics, the propagation of wave packets carrying intrinsic angular momentum is generally influenced by spin–orbit interactions. This is the main mechanism behind spin Hall effects, which result in wave packets following spin-dependent trajectories. Spin Hall effects have been observed in several experiments for electrons in condensed matter systems and for light propagating in inhomogeneous optical media. Similar effects have also been predicted for wave packets propagating in inhomogeneous gravitational fields. We give a brief introduction to gravitational spin Hall effects, emphasizing the analogies with the spin Hall effect of light in optics. Furthermore, we review the most promising astrophysical avenues that could lead to experimental observations of the gravitational spin Hall effect.

https://iopscience.iop.org/article/10.1088/1361-6382/ace021/pdf

Spin Hall effects in the sky

We revisit the motion of massless particles with anyonic spin in the horizon of Kerr--Newman geometry. As recently shown, such particles can move within the horizon of the black hole due to the coupling of charges associated with a 2-parametric central extension of the 2-dimensional Carroll group to the magnetic field generated by the black hole -- the so called"anyonic spin-Hall effect". We show that the previously computed magnetic field is not invariant under Carroll diffeomorphisms and find another result which respects these symmetries of the horizon. We also consider a more astrophysically relevant case of a (weakly charged) rotating back hole placed in a uniform magnetic field, which could, for instance, be induced by the surrounding plasma. We show that a qualitatively similar magnetic field assisted anyonic spin-Hall effect takes place, even in the absence of black hole rotation. The theoretical possibility of a motion induced by a magnetic monopole is also studied.

https://export.arxiv.org/pdf/2211.13695v2.pdf

Carrollian motion in magnetized black hole horizons

By considering a misaligned (asymptotically uniform) magnetic ﬁeld in the background of a rotating black hole, we uncover a possibility for a highly non-trivial motion of Carrollian particles on the black hole horizon that is characterized by a time-dependent velocity ﬁeld and is reminiscent of ‘monarch migration’

Monarch Migration of Carrollian Particles on the Black Hole Horizon

By considering a misaligned (asymptotically uniform) magnetic field in the background of a rotating black hole, we uncover a possibility for a highly non-trivial motion of Carrollian particles on the black hole horizon that is characterized by a time-dependent velocity field and reminds us (because of its latitudinal oscillations) of a 'monarch butterfly migration'.

Migrating Carrollian particles on magnetized black hole horizons

Using the fact that the horizon of black holes is a Carroll manifold, we show that an “exotic photon” i.e. a mass and chargeless particle with anyonic spin, magnetic moment and “exotic” charges associated with the 2-parameter central extension of the 2-dimensional Carroll group moves on the horizon of a Kerr-Newman Black Hole consistently with the Hall law, disproving the long-thought statement that Carroll particles cannot move.

Anyonic spin-Hall effect on the black hole horizon

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Anyonic spin-Hall effect on the black hole horizon