Birkhoff theorem

Every spherically symmetric vacuum solution of the Einstein field equation is locally a portion of Schwarzschild spacetime. In particular, a spherically symmetric body's exterior field depends only on its total mass.

A thin spherical shell of proper surface mass density $\rho$ held at Schwarzschild radius $r_{\mathrm{st}}$ around mass $M$ contributes, to first order in its mass,to the exterior Schwarzschild mass parameter.