Fields and fluids on curved non-relativistic spacetimes

Understand

We consider non-relativistic curved geometries and argue that the background structure should be generalized from that considered in previous works.

• In this approach the derivative operator is defined by a Galilean spin connection valued in the Lie algebra of the Galilean group.
• This includes the usual spin connection plus an additional "boost connection" which parameterizes the freedom in the derivative operator not fixed by torsion or metric compatibility.
• As an example we write down the most general theory of dissipative fluids consistent with the second law in curved non-relativistic geometries and find significant differences in the allowed transport coefficients from those found previously.