Surface density perturbation of a displaced uniform interface
= Surface density perturbation of a displaced uniform interface
{title2=$\rho^{\prime}=\rho_0\eta_+\delta(z-H)-\rho_0\eta_-\delta(z+H)$}
Moving a uniform-density boundary produces a delta-function sheet in the Eulerian <mass density> perturbation. For a slab displaced vertically by $\eta_\pm$, $\rho^{\prime}=\rho_0\eta_+\delta(z-H)-\rho_0\eta_-\delta(z+H)$. <Poisson equation> then gives a continuous gravitational potential with derivative jumps fixed by those sheets.