A cigar-like Universe

TL;DR

This paper constructs smooth, regular six-dimensional solutions describing a cigar-shaped universe with localized gravity on a string-like defect, revealing new geometric configurations with zero total energy.

Contribution

It provides the first complete numerical solutions for regular, cigar-like geometries in 6D with localized gravity, using BPS-like equations and supergravity potentials.

Findings

Solutions are regular everywhere with no deficit angle.

The geometry factorizes as AdS_5 times S_1 far from the core.

Total energy of configurations vanishes.

Abstract

We study the localization of gravity on a string-like topological defect within a 6-dimensional space-time. Assuming zero cosmological constant we find complete numerical solutions to a set of first-order, Bogomol'nyi-Prasad-Sommeferld (BPS)-like, equations for the metric and the scalar field, where the dynamics of the latter are dictated by a supergravity-type potential. Our axially symmetric solutions have no deficit angle and factorize as $AdS_5 \times S_1 $ far from the core. They are regular everywhere, providing complete smooth cigar-like geometries. The total energy of these configurations depends only on the boundary conditions for the warp factor and it is shown to vanish.