Linearized analysis of the Dvali–Gabadadze–Porrati brane model

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, this expression when confined on the physical brane reproduces the correct 4−D Newtonian potential for distances rs⪡r⪡λ, where λ is a characteristic length scale of the model, it does not coincide with the standard linearized form of the 4−D Schwarzschild metric. The solution reproduces the 5−D Schwarzschild metric in the linearized approximation for r⪢λ.