 Infinite gravitating particle lattice

An infinite gravitating particle lattice with spacing $h$ in the azimuthal direction is a shearing-sheet equilibrium when all particles sit at $x_n=0,y_n=nh$. Opposite-neighbor accelerations cancel absolutely. The linear gravitational response to pair displacement differences has transverse and longitudinal coefficients $1$ and $-2$, divided by $h^3|j-n{|}^3$.