Living Inside a Hedgehog: Higher-dimensional Solutions that Localize Gravity

TL;DR

This paper investigates higher-dimensional solutions in Einstein's equations with a cosmological constant, finding that localizing gravity with strictly local defects is not possible for three or more extra dimensions, but global defects and bulk magnetic fields can achieve localization.

Contribution

It demonstrates that local topological defects cannot localize gravity in higher dimensions, but global defects and bulk magnetic fields can, providing new insights into gravity localization mechanisms.

Findings

No gravity localization with local defects for n≥3

Global topological defects can localize gravity

Bulk magnetic fields lead to regular geometries and gravity localization

Abstract

We consider spherically symmetric higher-dimensional solutions of Einstein's equations with a bulk cosmological constant and n transverse dimensions. In contrast to the case of one or two extra dimensions we find no solutions that localize gravity when $n\geq 3$, for strictly local topological defects. We discuss global topological defects that lead to the localization of gravity and estimate the corrections to Newton's law. We show that the introduction of a bulk ``hedgehog'' magnetic field leads to a regular geometry and localizes gravity on the 3-brane with either a positive, zero or negative bulk cosmological constant. The corrections to Newton's law on the 3-brane are parametrically the same as for the case of one transverse dimension.