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There is significant recent work on coupling matter to Newton-Cartan spacetimes with the aim of investigating certain condensed matter phenomena. To this end, one needs to have a completely general spacetime consistent with local non-relativisitic symmetries, which supports massive matter fields. In particular, one cannot impose a priori restrictions on the geometric data if one wants to analyze matter response to a perturbed geometry. Dr. Roberts will construct such a Bargmann spacetime in complete generality without any prior restrictions on the fields specifying the geometry. The resulting spacetime structure includes the familiar Newton-Cartan structure with an additional gauge field, which couples to mass. We can use this technique to write locally Galilean invariant non-relativistic field theories and to construct Noether currents for the Galilean symmetries, in analogy with the stress-energy tensor in Lorentz invariant theories. We can also use this approach to derive equations of motion and constitutive relations for non-relativistic fluids at first order in dissipation.

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