  Given a maximal rigid object $T$ of the cluster tube, we determine the
objects finitely presented by $T$. We then use the method of Keller and Reiten
to show that the endomorphism algebra of $T$ is Gorenstein and of finite
representation type, as first shown by Vatne. This algebra turns out to be the
Jacobian algebra of a certain quiver with potential, when the characteristic of
the base field is not 3. We study how this quiver with potential changes when
$T$ is mutated. We also provide a derived equivalence classification for the
endomorphism algebras of maximal rigid objects.
