DGP Brane as a Gravity Conductor

TL;DR

This paper investigates how the DGP brane influences particle behavior, revealing that particles are naturally repelled into the bulk due to self-energy considerations, with implications for gravity localization and black hole formation.

Contribution

It introduces a classical analysis of particle self-energy in DGP brane models, showing universal repulsion from the brane and connecting gravitational effects to electrostatic analogies.

Findings

Particles are repelled from the brane due to self-energy minimization.

The brane acts as a conducting plane in electrostatic analogy, causing charge shielding.

Particles with mass above a threshold form black holes near the brane.

Abstract

We study how the DGP (Dvali-Gabadadze-Porrati) brane affects particle dynamics in linearized approximation. We find that once the particle is removed from the brane it is repelled to the bulk. Assuming that the cutoff for gravitational interaction is $M_*\sim 1/\epsilon$, we calculate the classical self energy of a particle as the function of its position. Since the particle wants to go to the region where its self energy is lower, it is repelled from the brane to the bulk where it gains its 5D self energy. Cases when mass of the particle $m<8\pi^2M_*$ and $m>8\pi^2M_*$ are qualitatively different, and in later case one has to take into account effects of strong gravity. In both cases the particle is repelled from the brane. For $m<8\pi^2M_*$ we obtain the same result from the 'electrostatic' analog of the theory. In that language mass (charge) in the bulk induces charge distribution on the brane which shields the other side of the brane and provides repulsive force. The DGP brane acts as a conducting plane in electrostatics (keeping in mind that in gravity different charges repel). The repulsive nature of the brane requires a certain localization mechanism. When the particle overcomes the localizing potential it rapidly moves to the bulk. Particles of mass $m>8\pi^2M_*$ form a black hole within $1/M_*$ distance from the brane.