  The aim of this paper is to elucidate a close connection between the black
hole area law and the infinite distance conjecture in the context of the
swampland. We consider families of black hole geometries, parametrized by their
event horizon areas or by the values of their entropies, and show that the
infinite entropy limit is always at infinite distance in the space of black
hole geometries. It then follows from the infinite distance conjecture that
there must be a tower of states in the infinite entropy limit, and that
ignoring these towers on the horizon of the black hole would invalidate the
effective theory when the entropy becomes large. We call this the black hole
entropy distance conjecture. We then study two candidates for the tower of
states. The first are the Kaluza-Klein modes of the internal geometry of
extremal ${\cal N}=2$ black holes in string theory, whose masses on the horizon
are fixed by the ${\cal N}=2$ attractor formalism, and given in terms of the
black hole charges similarly to the entropy. However, we observe that it is
possible to decouple their masses from the entropy, so that they cannot
generically play the role of the tower. We thus consider a second kind of
states: inspired by N-portrait quantum models of non-extremal black holes, we
argue that the Goldstone-like modes that interpolate among the black hole
microstates behave like the expected light tower of states.
