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Recently, a non-relativistic off-shell formulation of three dimensionalNewton-Cartan supergravity was proposed as the $c \rightarrow \infty$ limit ofthree dimensional $\mathcal{N}=2$ supergravity in arXiv:1505.02095. In thepresent paper we study supersymmetric backgrounds within this theory. Usingintegrability constraints for the non-relativistic Killing spinor equations, weexplicitly construct all maximally supersymmetric solutions, which admit foursupercharges. In addition to these solutions, there are $\frac{1}{2}$-BPSsolutions with reduced supersymmetry. We give explicit examples of suchbackgrounds and derive necessary conditions for backgrounds preserving twosupercharges. Finally, we address how supersymmetric backgrounds of$\mathcal{N}=2$ supergravity are connected to the solutions found here in the$c \rightarrow \infty$ limit.

Rigid Supersymmetric Backgrounds of 3-dimensional Newton-Cartan Supergravity