Newton-Cartan, Galileo-Maxwell and Kaluza-Klein

TL;DR

This paper explores Kaluza-Klein reduction within Newton-Cartan gravity, revealing that dimensional reduction and nonrelativistic limits commute, leading to a novel nonrelativistic theory with coupled scalar and vector matter affecting spatial curvature.

Contribution

It presents the first example of back-reacted couplings of scalar and vector matter to Newton-Cartan gravity, demonstrating the nontrivial influence on spatial Ricci curvature.

Findings

Dimensional reduction and nonrelativistic limit commute.

The resulting theory includes Galilean electromagnetism and a scalar.

Back-reaction sources spatial Ricci curvature.

Abstract

We study Kaluza-Klein reduction in Newton-Cartan gravity. In particular we show that dimensional reduction and the nonrelativistic limit commute. The resulting theory contains Galilean electromagnetism and a nonrelativistic scalar. It provides the first example of back-reacted couplings of scalar and vector matter to Newton-Cartan gravity. This back-reaction is interesting as it sources the spatial Ricci curvature, providing an example where nonrelativistic gravity is more than just a Newtonian potential.