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.
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