%0 Journal Article
%T Graphene and the Zermelo Optical Metric of the BTZ Black Hole
%A M. Cvetic
%A G. W. Gibbons
%J Physics
%D 2012
%I arXiv
%R 10.1016/j.aop.2012.05.013
%X 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.
%U http://arxiv.org/abs/1202.2938v2