Black-Hole-Like Saturons in Gross-Neveu

TL;DR

This paper demonstrates that saturons in the Gross-Neveu model exhibit black hole-like properties, including entropy scaling, thermal decay, and information retrieval times, linking unitarity saturation to black hole physics.

Contribution

It shows that saturons in a simple quantum field theory model possess properties analogous to black holes, including entropy scaling and thermal decay.

Findings

Saturons in Gross-Neveu model have entropy scaling similar to Bekenstein-Hawking entropy.

Bound states exhibit thermal decay rates consistent with Hawking radiation.

Information retrieval times match Page's time, indicating black hole-like information dynamics.

Abstract

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.