Eguchi-Hanson Solitons in Odd Dimensions

TL;DR

This paper introduces a new class of Lorentzian Eguchi-Hanson-like solutions in odd-dimensional Einstein's equations with (A)dS asymptotics, revealing their energy properties and potential ground state status.

Contribution

It extends Eguchi-Hanson metrics to odd dimensions with Lorentzian signatures and analyzes their energy and stability properties in (A)dS backgrounds.

Findings

Solutions are asymptotic to (A)dS/Z_p.

In AdS, solutions have negative energy relative to pure AdS.

In dS, solutions have mass less than pure dS at future infinity.

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-(A)dS metrics, with the added feature of having Lorentzian signatures. They are asymptotic to (A)dS$_{d+1}/Z_p$. In the AdS case their energy is negative relative to that of pure AdS. We present perturbative evidence in 5 dimensions that such metrics are the states of lowest energy in their asymptotic class, and present a conjecture that this is generally true for all such metrics. In the dS case these solutions have a cosmological horizon. We show that their mass at future infinity is less than that of pure dS.