  We study the possible existence of a Newtonian regime of gravity in $1+1$
dimensions, considering metrics in both the Kerr-Schild and conformal forms. In
the former case, the metric gives the exact solution of the Poisson equation in
flat space, but the weak-field limit of the solutions and the non-relativistic
regime of geodesic motion are not trivial. We show that using harmonic
coordinates, the metric is conformally flat and a weak-field expansion is
straightforward. An analysis of the non-relativistic regime of geodesic motion
remains non-trivial and the weak-field potential only satisfies the flat space
Poisson equation approximately.
