Galilean and Carrollian Hodge star operators
arXiv:2206.09788 · doi:10.1016/S0034-4877(24)00007-7
Abstract
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.
Version published in Reports on Mathematical Physics (plus Content)
References in corpus (5)
- Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time
- Carroll/fracton particles and their correspondence
- Interacting Conformal Carrollian Theories: Cues from Electrodynamics
- Some useful operators on differential forms in Galilean and Carrollian spacetimes
- Beyond Lorentzian Symmetry