  There is currently significant interest in emulating the essential
characteristics of black holes, such as their Hawking radiation or their
optimal scrambling behavior, using condensed matter models. In this article, we
investigate a chiral spin-chain, whose mean field theory effectively captures
the behavior of Dirac fermions in the curved spacetime geometry of a black
hole. We find that within the region of the chain that describe the interior of
the black hole, strong correlations prevail giving rise to many-body chaotic
dynamics. Employing out-of-time-order correlations as a diagnostic tool, we
numerically compute the associated Lyapunov exponent. Intriguingly, we observe
a linear increase in the Lyapunov exponent with temperature within the black
hole's interior at low temperatures, indicative of optimal scrambling behavior.
This contrasts with the quadratic temperature dependence exhibited by the
spin-chain on the region outside the black hole. Our findings contribute to a
deeper understanding of the interplay between black hole geometry and quantum
chaos, offering insights into fundamental aspects of quantum gravity.
