Eguchi–Hanson solitons in odd dimensions

Abstract

We present a new class of solutions in odd dimensions to Einstein's equations containing either a positive or a 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)dSd+1/Zp. In the AdS case, their energy is negative relative to that of pure AdS. We present perturbative evidence in five 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.