Non-relativistic Limits of General Relativity

Summary: The discussion focuses on a specific non-relativistic limit of NS-NS gravity that can be achieved at the level of the action and equations of motion without imposing any geometric constraints manually. The cancellation of divergences between terms that arise from the Vielbein in the Einstein-Hilbert term and from the kinetic term of the Kalb-Ramond two-form field is key to this limit. This leads to the emergence of a local target space scale invariance in the limit, resulting in an extra equation in the equations of motion compared to the action limit. The geometric constraints that can be solved by scale-invariant constraints define a Dilatation invariant String Newton-Cartan geometry.