  The standard Hodge star operator is naturally associated with metric tensor
(and orientation). It is routinely used to concisely write down physics
equations on, say, Lorentzian spacetimes. On Galilean (Carrollian) spacetimes,
there is no canonical (nonsingular) metric tensor available. So, the usual
construction of the Hodge star does not work. Here we propose analogs of the
Hodge star operator on Galilean (Carrollian) spacetimes. They may be used to
write down important physics equations, e.g. equations of Galilean (Carrollian)
electrodynamics.
