1202.2938 (M. Cvetic et al.)

Graphene and the Zermelo Optical Metric of the BTZ Black Hole    [PDF]

M. Cvetic, G. W Gibbons

We argue 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 magnetic field on the graphene sheet induces a gauge potential on the
world volume of the membrane 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. We show that there
is fundamental geometric obstacle to obtain a model that extends all the way to
the black hole horizon.

View original: http://arxiv.org/abs/1202.2938