  We compute the Rabinowitz Floer homology for a class of non-compact
hyperboloids $\Sigma\simeq S^{n+k-1}\times\mathbb{R}^{n-k}$. Using an embedding
of a compact sphere $\Sigma_0\simeq S^{2k-1}$ into the hypersurface $\Sigma$,
we construct a chain map from the Floer complex of $\Sigma$ to the Floer
complex of $\Sigma_0$. In contrast to the compact case, the Rabinowitz Floer
homology groups of $\Sigma$ are both non-zero and not equal to its singular
homology. As a consequence, we deduce that the Weinstein Conjecture holds for
any strongly tentacular deformation of such a hyperboloid.
