Newtonian Gravity and the Bargmann Algebra

Details Newtonian Gravity and the Bargmann Algebra Newtonian Gravity and the Bargmann Algebra

2010-11-04

arxiv.org/abs/1011.1145v3

Class.Quant.Grav.28:105011,2011

Physics

High Energy Physics

High Energy Physics - Theory

Latex, 20 pages, typos corrected, published version

Scientific paper

10.1088/0264-9381/28/10/105011

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. In the final step we impose an additional curvature constraint to establish the connection with (on-shell) Newton-Cartan theory. We discuss a few extensions of our work that are relevant in the context of the AdS-CFT correspondence.

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