Curved non-relativistic spacetimes, Newtonian gravitation and massive matter
Abstract
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 can not impose a priori restrictions on the geometric data if one wants to analyze matter response to a perturbed geometry. In this paper we 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 illustrate the matter coupling with a few examples. The general spacetime we construct also includes as a special case the covariant description of Newtonian gravity, which has been thoroughly investigated in previous works. We also show how our Bargmann spacetimes arise from a suitable non-relativistic limit of Lorentzian spacetimes. In a companion paper [arXiv:1503.02680] we use this Bargmann spacetime structure to investigate the details of matter couplings, including the Noether-Ward identities, and transport phenomena and thermodynamics of non-relativistic fluids.
Keywords
Cite
@article{arxiv.1503.02682,
title = {Curved non-relativistic spacetimes, Newtonian gravitation and massive matter},
author = {Michael Geracie and Kartik Prabhu and Matthew M. Roberts},
journal= {arXiv preprint arXiv:1503.02682},
year = {2015}
}
Comments
v5: update references. matches version published in JMP v4: minor text changes. version accepted in Journal of Mathematical Physics v3: improved discussion of NR limit and added refs, v2: updated references and text. v1: 39 pages, 2 figures