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We investigate the consequences of Birkhoff's theorem in general relativity(GR) and in Modified Newtonian dynamics (MOND). We study, in particular, thesystem of a finite-mass test particle inside a spherical shell. In both GR andMOND, we find non-vanishing acceleration for that test particle. The directionof the acceleration is such that it pushes the test particle toward the centerof the shell. In GR, the acceleration is found analytically in the case of asmall test mass with a small displacement from the center of the shell. InMOND, the acceleration is found analytically in the limit of large test massand small displacement, and a comparison to numerical values is made. Numericalsimulations are done for more general cases with parameters that mimic thesystem of a galaxy in a cluster. In GR, the acceleration is highly suppressed,and physically insignificant. In MOND, on the contrary, the acceleration of thepoint particle can be a significant fraction of the field just outside of thespherical shell.

Birkhoff's theorem fails to save MOND from non-local physics