Graphene and the Zermelo optical metric of the BTZ black hole
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA 19104-6396 (United States)
- D.A.M.T.P., University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom)
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 R Multiplication-Sign {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 a fundamental geometric obstacle to obtaining a model that extends all the way to the black hole horizon. - Highlights: Black-Right-Pointing-Pointer Electrons on graphene sheets obey the Dirac equation in ultra-static metrics. Black-Right-Pointing-Pointer External magnetic fields on give ultra-stationary metrics. Black-Right-Pointing-Pointer These metrics are of optical-Zermelo form. Black-Right-Pointing-Pointer Embedded surfaces corresponding to BTZ black holes are given.
- OSTI ID:
- 22157109
- Journal Information:
- Annals of Physics (New York), Vol. 327, Issue 11; Other Information: Copyright (c) 2012 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); ISSN 0003-4916
- Country of Publication:
- United States
- Language:
- English
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