Non-relativistic limits and 3D massive gravity

The non-relativistic version of General Relativity, called Newton-Cartan gravity, has received renewed attention as a tool to explore (non-perturbative) properties of nonrelativistic quantum field theories. The first part of this talk is a non-specialist introduction to Newton-Cartan geometry; in particular, it is shown how Newton-Cartan gravity arises as a special limit of General Relativity. The second part reviews a novel non-relativistic limit of the 3D massive spin-2 Fierz-Pauli theory to a spin-2 planar Schrodinger equation that has been proposed to describe the so-called GMP gapped spin-2 mode of fractional Quantum Hall states. The talk concludes with speculations on an extension of this non-relativistic limit to interacting massive 3D gravity theories.