Self-gravitating incompressible slab
= Self-gravitating incompressible slab
{title2=$\rho_0=\Sigma/(2H)$}
A uniform <mass density> slab with free surfaces at $z=\pm H$ has $\rho_0=\Sigma/(2H)$, internal gravity $4\pi G\rho_0z$ and hydrostatic <pressure> $2\pi G\rho_0^2(H^2-z^2)$ above ambient <pressure>. Its <surface modes of a self-gravitating incompressible slab> separate into thickness and bending parities.