Black-Hole-Like Saturons in Gross-Neveu

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.