Newton-Cartan, Galileo-Maxwell and Kaluza-Klein

Understand

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.