= Gravitational potential of a displaced cylindrical interface
{title2=$\Phi'(R_0)=-2\pi G\rho_0R_0\eta/m,\quad m\geq1$}
For a uniform-<mass density> cylinder with surface displacement $\eta e^{im\phi}$, the interior and exterior potential perturbations solve <Laplace's equation> and are proportional to $R^m$ and $R^{-m}$. Continuity of potential and the Poisson derivative jump $\Phi'_{R,\mathrm{out}}-\Phi'_{R,\mathrm{in}}=4\pi G\rho_0\eta$ give the displayed surface amplitude. The surface <mass density> term must be retained even though bulk incompressibility makes the interior <mass density> perturbation zero.
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