  It has been argued recently that objects of maximal microstate entropy
permitted by unitarity, the so-called saturons, have properties similar to
black holes. We demonstrate the existence of such objects in Gross-Neveu model.
From the large-$N$ scaling of $S$-matrix, we deduce the connection between the
entropy of the bound-state and the unitarity of scattering. We observe that
upon saturation of unitarity, the bound state exhibits a remarkable
correspondence with a black hole. The scaling of its entropy is identical to
Bekenstein-Hawking entropy. The saturon decays via Hawking's thermal rate of
temperature given by the inverse size. The information retrieval time from the
Gross-Neveu saturon is isomorphic to Page's time. Our observations indicate
that black hole properties are exhibited by saturated states in simple
calculable models.
