Soliton Solutions to the Einstein Equations in Five Dimensions

TL;DR

This paper introduces new Lorentzian solutions to Einstein's equations in five dimensions with a cosmological constant, demonstrating they are likely the lowest-energy states asymptotic to AdS$_{5}/ ext{Gamma}$.

Contribution

It provides the first known solutions in five dimensions with negative cosmological constant that are asymptotically AdS and have lower energy than the standard AdS background.

Findings

Solutions resemble higher-dimensional Eguchi-Hanson-(A)dS metrics

Existence of solutions with negative cosmological constant and lower energy than AdS$_{5}/ ext{Gamma}$

Evidence suggests these are the lowest-energy states in their class

Abstract

We present a new class of solutions in odd dimensions to Einstein's equations containing either a positive or negative cosmological constant. These solutions resemble the even-dimensional Eguchi-Hanson--(anti)-de Sitter ((A)dS) metrics, with the added feature of having Lorentzian signatures. They provide an affirmative answer to the open question as to whether or not there exist solutions with negative cosmological constant that asymptotically approach AdS$_{5}/\Gamma$, but have less energy than AdS$_{5}/\Gamma$. We present evidence that these solutions are the lowest-energy states within their asymptotic class.