# Mass of collapsing spherical shell

For a thin spherical shell of mass $$M$$ collapsing to a Schwarzschild black hole, the Birkhoff's theorem ensures that outside is Schwarzschild metric. Then the ADM mass of this spacetime is just constant $$M$$ during the whole collapse. However, physically one expects the infalling mass shell have decreasing gravitational potential energy and hence the total energy (mass of the shell+gravitational potential energy) of spacetime should decrease. How do we resolve the tension? Does it implies as the collapse goes, the shell is getting heavier and heavier?