  It is well known that the low energy electron excitations of the curved
graphene sheet $\Sigma$ are solutions of the massless Dirac equation on a 2+1
dimensional ultra-static metric on ${\Bbb R} \times \Sigma$. An externally
applied electric field on the graphene sheet induces a gauge potential which
could be mimicked by considering a stationary optical metric of the Zermelo
form, which is conformal to the BTZ black hole when the sheet has a constant
negative curvature. The Randers form of the metric can model a magnetic field,
which is related by a boost to an electric one in the Zermelo frame. We also
show that there is fundamental geometric obstacle to obtaining a model that
extends all the way to the black hole horizon.
