Radion Stabilization in Compact Hyperbolic Extra Dimensions

TL;DR

This paper investigates the challenges of stabilizing extra dimensions in hyperbolic brane-world models, revealing that matter fields required for stabilization must violate energy conditions, with potential solutions discussed.

Contribution

It demonstrates that matter fields stabilizing hyperbolic extra dimensions must violate the null energy condition within Einstein gravity, highlighting a fundamental obstacle in such models.

Findings

Stabilizing matter fields violate null energy condition

Explicit demonstration of failed stabilization sources

Discussion of Casimir energy as a potential bypass

Abstract

We consider radion stabilization in hyperbolic brane-world scenarios. We demonstrate that in the context of Einstein gravity, matter fields which stabilize the extra dimensions must violate the null energy condition. This result is shown to hold even allowing for FRW-like expansion on the brane. In particular, we explicitly demonstrate how one putative source of stabilizing matter fails to work, and how others violate the above condition. We speculate on a number of ways in which we may bypass this result, including the effect of Casimir energy in these spaces. A brief discussion of supersymmetry in these backgrounds is also given.