Modified Gravity: living without Birkhoff I. DGP

TL;DR

This paper explores the effects of lacking Birkhoff's theorem in modified gravity theories, specifically analyzing the DGP model where gravitational force depends on mass distribution and bulk geometry.

Contribution

It demonstrates how the absence of Birkhoff's theorem in DGP modifies gravitational force behavior compared to General Relativity.

Findings

Gravitational force depends on mass distribution in DGP.

Force within a spherical shell depends on bulk geometry.

Birkhoff's theorem does not hold in the studied modified gravity model.

Abstract

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-Gabadaze-Porrati model (DGP). 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 non-zero.