Observational Cosmology - Unit 2 Solutions
2. In an island universe the force from external shells will not vanish, so the analysis will fail at the stage where Newton's (or strictly Birkhoff's) Theorem is invoked. Remember that in a uniform density universe, the mass in a shell of thickness dr scales as r2dr, so the force from distant shells (which scales as Mshell/r2) is potentially important if the shell is incomplete.