Consider a perfectly spherical dust shell with a large internal cavity. Imagine there is a moment when the dust is momentarily stationary and there is a string of clocks strung out along a radial axis. At this instant, I will assume that the spacetime inside the cavity is flat and all the clocks inside the cavity are synchronised with each other and ticking at the same rate as each other, but ticking slower than clocks outside the cavity. If we take a 'snapshots' at later stages of the collapse, and consider only the ticking rate of a clock that happens to be at the inner surface of the shell (before it gets swept along by the dust) then the ticking rate of of each representative clock will be even slower than the previous representative clock, relative to the one at infinity. This slightly elaborate set up of representative clocks rather than a single clock co-moving with the inner surface, is to avoid the complications due to the motion of such a clock. Since the outermost clock of the cavity at any given stage of the collapse is ticking slower than the outermost clocks at earlier stages, this change has to propagate into the cavity if we want the spacetime to remain flat inside the cavity and have all the clocks inside the cavity ticking at the same rate. Now the difficulty is that this propagation of changes in the field, into the cavity can only happen at a finite speed, so it appears there will inevitably be a gravitational gradient within the cavity. Clocks at outermost part of the cavity will be ticking slower than clocks near the centre of the cavity, because the innermost clocks are not yet 'aware' of the changes. This gradient would be from a high potential near the centre to a lower potential near the inner surface of the cavity. This suggests test particles inside the shell might start falling outwards towards the collapsing shell due the gravitational gradient. Now I am aware that there will be issues due to the various notions of simultaneity, but I am not sure how this is resolved and would be interested in any opinions on this. Another approach to eliminating gradient issues within the cavity is to assume the velocity of the collapsing dust conspires with the mass of the dust in such a way that the time dilation at the inner surface of the cavity remains constant at any stage of the collapse, but I am not sure that is what actually happens. I am also aware that the Oppenheimer-Snyder pressureless dust solution, sort of addresses this situation, but it is from the point of view of an observer co-falling with the dust and it's only applicable to a sphere of dust, rather than a sphere with a cavity. Any thoughts on what happens inside the cavity in this dynamic situation? P.S. To quote Wikipedia Birkhoff's theorem implies: That statement does not make it clear if that conclusion only applies to a static shell or not.