Newtonian Gravity and the Bargmann Algebra

Understand

We show how the Newton-Cartan formulation of Newtonian gravity can be obtained from gauging the Bargmann algebra, i.e., the centrally extended Galilean algebra.

• In this gauging procedure several curvature constraints are imposed.
• These convert the spatial (time) translational symmetries of the algebra into spatial (time) general coordinate transformations, and make the spin connection gauge fields dependent.
• In addition we require two independent Vielbein postulates for the temporal and spatial directions.