= Frame dragging inside a slowly rotating spherical shell
{title2=$\omega=\frac{4GM}{3R}\Omega$}
For a weakly gravitating thin spherical shell of mass $M$, radius $R$ and uniform angular velocity $\Omega$, its interior <linearized gravity> metric has constant scalar potentials $A=-GM/R$, $C=GM/R$ and $g_{0i}=\omega(\widehat{\mathbf z}\times\mathbf x)_i$. The scalar mass shell is a monopole. Its mass current is a dipole: regular interior and decaying exterior radial solutions are proportional to $r$ and $r^{-2}$, and their derivative jump fixes the factor $4/3$. Local inertial axes co-rotate with the shell at $\omega$ relative to asymptotic nonrotating axes. This is the leading interior <Lense-Thirring precession>, neglecting quadratic rotation and higher gravitational orders.
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