  This paper connects two different approaches to the analysis of Hamiltonian
dynamics on non-compact energy hypersurfaces - $b$-symplectic geometry with its
singular symplectic form and Floer techniques for tentacular Hamiltonians. More
precisely, we show how to equip tentacular hyperboloids with a $b$-contact
structure. We construct a $b^3$-symplectic manifold $(X, Z, \omega_b)$, such
that each connected component of $X\setminus Z$ is symplectomorphic to the
standard symplectic space $(T^*\mathbb{R}^n, \omega_0)$. For a tentacular
hyperboloid $S \subseteq T^*\mathbb{R}^n$ we look at its copies in $X \setminus
Z$ and show that their completion in $(X,Z, \omega_b)$ is a smooth hypersurface
of $b$-contact type.
