I present 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$_{5}/\Gamma$. I shall outline how these solutions are obtained and will present evidence that these solutions are the lowest-energy states within their asymptotic class. As such, they may furnish a new class of ground states to string theory and as the endstate of tachyon condensation.