Schwarzschild solution in brane induced gravity

TL;DR

This paper investigates a nonperturbative Schwarzschild solution in five-dimensional brane induced gravity, revealing mass screening effects, a smooth recovery of 4D gravity, and the absence of the vDVZ discontinuity.

Contribution

It provides an exact nonperturbative solution on the brane and demonstrates how nonlinear interactions lead to mass screening and consistent four-dimensional gravity.

Findings

The ADM mass is suppressed compared to the bare mass.

The solution exhibits no vDVZ discontinuity.

Four-dimensional gravity is recovered at observable scales.

Abstract

The metric of a Schwarzschild solution in brane induced gravity in five dimensions is studied. We find a nonperturbative solution for which an exact expression on the brane is obtained. We also find a linearized solution in the bulk and argue that a nonsingular exact solution in the entire space should exist. The exact solution on the brane is highly nontrivial as it interpolates between different distance scales. This part of the metric is enough to deduce an important property -- the ADM mass of the solution is suppressed compared to the bare mass of a static source. This screening of the mass is due to nonlinear interactions which give rise to a nonzero curvature outside the source. The curvature extends away from the source to a certain macroscopic distance that coincides with the would-be strong interaction scale. The very same curvature shields the source from strong coupling effects. The four dimensional law of gravity, including the correct tensorial structure, is recovered at observable distances. We find that the solution has no vDVZ discontinuity and show that the gravitational field on the brane is always weak, in spite of the fact that the solution is nonperturbative.