  During the final stages of black hole evaporation, ultraviolet deviations
from General Relativity eventually become dramatic, potentially affecting the
end-state. We explore this problem by performing nonlinear simulations of wave
packets in Einstein-dilaton-Gauss-Bonnet gravity, the only gravity theory with
quadratic curvature terms which can be studied at fully nonperturbative level.
Black holes in this theory have a minimum mass but also a nonvanishing
temperature. This poses a puzzle concerning the final fate of Hawking
evaporation in the presence of high-curvature nonperturbative effects. By
simulating the mass loss induced by evaporation at the classical level using an
auxiliary phantom field, we study the nonlinear evolution of black holes past
the minimum mass. We observe a runaway shrink of the horizon (a nonperturbative
effect forbidden in General Relativity) which eventually unveils a
high-curvature elliptic region. While this might hint to the formation of a
naked singularity (and hence to a violation of the weak cosmic censorship) or
of a pathological spacetime region, a different numerical formulation of the
initial-value problem in this theory might be required to rule out other
possibilities, including the transition from the critical black hole to a
stable horizonless remnant. Our study is relevant in the context of the
information-loss paradox, dark-matter remnants, and for constraints on
microscopic primordial black holes.
