  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.
