On Newtonian knot in empty (2+1)-dimensional space-time

We propose the existence of a topological object, a Newtonian knot, in the framework of an Abelian Chern-Simons gravity with a small positive cosmological constant in empty (2+1)-dimensional space-time. This proposal is based on the idea that the Ricci curvature tensor could consist of a set of curvature components satisfying the non-trivial Hopf maps, leading to topological structures. Working within the Abelian Chern-Simons (first-order) framework, where the dreibein and spin connection are treated as independent fields, we derive the corresponding field equations and present ansatz solutions for both. Our results suggest that the Newtonian knot may serve as a novel topological feature in low-dimensional gravity theories.