%0 Journal Article %1 Cvetic2012Graphene %A Cvetic, M. %A Gibbons, G. W. %D 2012 %K ads-cmt, ads3-cft2, arxiv %T Graphene and the Zermelo Optical Metric of the BTZ Black Hole %U http://arxiv.org/abs/1202.2938 %X 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 \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.

@article{Cvetic2012Graphene, abstract = {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.}, added-at = {2019-02-26T10:37:35.000+0100}, archiveprefix = {arXiv}, author = {Cvetic, M. and Gibbons, G. W.}, biburl = {https://www.bibsonomy.org/bibtex/2ad4244dbd7f5fab126914d4f0ac2261c/acastro}, citeulike-article-id = {10353764}, citeulike-linkout-0 = {http://arxiv.org/abs/1202.2938}, citeulike-linkout-1 = {http://arxiv.org/pdf/1202.2938}, day = 14, eprint = {1202.2938}, interhash = {e45a673b2a751eb6c96037e139950659}, intrahash = {ad4244dbd7f5fab126914d4f0ac2261c}, keywords = {ads-cmt, ads3-cft2, arxiv}, month = feb, posted-at = {2012-02-15 11:37:50}, priority = {2}, timestamp = {2019-02-26T10:37:35.000+0100}, title = {{Graphene and the Zermelo Optical Metric of the BTZ Black Hole}}, url = {http://arxiv.org/abs/1202.2938}, year = 2012 }