Newton-Cartan, Galileo-Maxwell and Kaluza-Klein
arXiv:1512.03799 · doi:10.1088/0264-9381/33/13/137002
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.
Few typos corrected and comments added. Version accepted for publication + additional refs
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- Oddity in nonrelativistic, strong gravity
- Galilean Gauge Theories from Null Reductions
- Galilean Field Theories and Conformal Structure
- New formulation of Galilean relativistic Maxwell theory
- Galilean Electrodynamics: Covariant formulation and Lagrangian
- Galilean and Carrollian Hodge star operators
- Gauge interactions and the Galilean limit