Consequences of the absence of Birkhoff's theorem in modified-gravity theories: The Dvali-Gabadaze-Porrati model

We consider the consequences of the absence of Birkhoff's theorem in theories of modified gravity. As an example, we calculate the gravitational force on a test particle due to a spherical mass shell in the Dvali-Gabadadze-Porrati model. We show that unlike in general relativity, the force depends on the mass distribution. In particular, the gravitational force within a spherical mass shell depends on the geometric structure of the bulk, and is likely nonzero.