Graphene and the Zermelo Optical Metric of the BTZ Black Hole

Details Graphene and the Zermelo Optical Metric of the BTZ Black Hole Graphene and the Zermelo Optical Metric of the BTZ Black Hole

2012-02-14

arxiv.org/abs/1202.2938v1

Physics

High Energy Physics

High Energy Physics - Theory

9 pages Latex, no figures

Scientific paper

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.

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