Linearized Analysis of the Dvali-Gabadadze-Porrati Brane Model

TL;DR

This paper derives an exact first-order gravitational field solution in the Dvali-Gabadadze-Porrati brane model for static, spherically symmetric matter, revealing deviations from standard 4D Schwarzschild behavior at certain scales.

Contribution

It provides an exact linearized solution for the gravitational field in the DGP model, clarifying the transition between 4D and 5D gravitational regimes.

Findings

Reproduces 4D Newtonian potential for intermediate scales

Deviates from standard Schwarzschild metric at small scales

Matches 5D Schwarzschild in the linearized limit for large scales

Abstract

We solve the Einstein equations in the Dvali-Gabadadze-Porrati model with a static, spherically symmetric matter distribution on the physical brane and obtain an exact expression for the gravitational field outside the source to the first order in the gravitational coupling. Although when confined on the physical brane this expression reproduces the correct 4D Newtonian potential for distances r_s << r << {\lambda}, where {\lambda} is a characteristic length scale of the model, it does not coincide with the standard linearized form of the 4D Schwarzschild metric. The solution reproduces the 5D Schwarzschild metric in the linearized approximation for r >> {\lambda}.