The Schwarzschild solution in the DGP model

TL;DR

This paper derives the Schwarzschild solution within the DGP model using a perturbative approach that remains valid near the Schwarzschild radius, showing the absence of vDVZ discontinuity and matching the standard solution on the brane.

Contribution

It provides the explicit form of the Schwarzschild solution in the DGP model, including off-diagonal metric terms, and demonstrates its non-singular behavior near the Schwarzschild radius.

Findings

The solution matches the standard Schwarzschild metric on the brane.

The perturbative expansion is valid both far from and near the Schwarzschild radius.

The model shows no vDVZ discontinuity, indicating a smooth massless limit.

Abstract

We discuss the Schwarzschild solution in the Dvali-Gabadadze-Porrati (DGP) model. We obtain a perturbative expansion and find the explicit form of the lowest-order contribution. By keeping off-diagonal terms in the metric, we arrive at a perturbative expansion which is valid both far from and near the Schwarzschild radius. We calculate the lowest-order contribution explicitly and obtain the form of the metric both on the brane and in the bulk. As we approach the Schwarzschild radius, the perturbative expansion yields the standard four-dimensional Schwarzschild solution on the brane which is non-singular in the decoupling limit. This non-singular behavior is similar to the Vainshtein solution in massive gravity demonstrating the absence of the van Dam-Veltman-Zakharov (vDVZ) discontinuity in the DGP model.