Consider a sphere with outer radius r2 and a centred inner cavity of radius r1, forming a constant density shell with density p. Let's say the time dilation on a clock on the inner surface of the shell is ta. Now the shell with filled with a material of the same constant density as the shell such that the time dilation factor due to the material that fills the cavity is tb = √(1-2*p*4/3*pi*r12). If we ignore the time dilation due to the material in the original shell. Would the total time dilation factor at r1 due to the material in the filled inner cavity and the material in the outer shell, be equal to ta*tb? Starting again with original hollow shell and a clock at r1, an additional shell with the same constant density and inner radius of r2 and outer radius r3 now encloses the original shell. If the time dilation on the clock at r1, due to the new outer shell alone is tc, would the combined time dilation acting on the clock at r1 due to both shells be ta*tc or does time dilation combine in some other way? From my initial investigations, time dilation does not seem to combine as a simple product (or sum) and the time dilation due to an outer shell, does not seem to have a time dilation component that is independent of material inside the cavity. Can anyone shed any light (or equations) on these issues?