Flat 3-Brane with Tension in Cascading Gravity

TL;DR

In the cascading gravity brane-world scenario, this work shows that a 3-brane with tension remains flat, at least for sufficiently small tension that the weak-field approximation is valid.

Abstract

In the Cascading Gravity brane-world scenario, our 3-brane lies within a succession of lower-codimension branes, each with their own induced gravity term, embedded into each other in a higher-dimensional space-time. In the 6+1-dimensional version of this scenario, we show that a 3-brane with tension remains flat, at least for sufficiently small tension that the weak-field approximation is valid. The bulk solution is nowhere singular and remains in the perturbative regime everywhere.

Figures (2)

• Figure 1: Sketch of the codimension-3 cascading gravity set-up.
• Figure 2: Plot of the solution for the metric potential $\hat{\Phi}(y,z,w)$ for $w=0$ and $w=2m_7^{-1}$ in the case where $m_6=m_7$.