2012/02/29 by M. Cvetič, M. Cvetic, G.W Gibbons +1 · 89 citations
Physics and Astronomy · #Advanced Differential Geometry Research #BTZ black hole #Black Holes and Theoretical Physics #Black hole (networking) #Charged black hole #Conformal map #Dirac equation #Electric field #Extremal black hole #Graphene #Massless particle #Metric (unit) #Noncommutative and Quantum Gravity Theories #cond-mat.mtrl-sci #gr-qc #hep-th
paper · pdf · doi:10.1016/j.aop.2012.05.013
published in Annals of Physics 327(11), 2617-2626 (Elsevier BV) · 10 pages Latex, no figures, substantial revisions, relation between magnetic and electric fields and Randers and Zermelo forms clarified
arxiv created 2012/05/23 · openalex publication_date 2012/06/08 · arxiv updated 2015/06/04 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
It is well known that the low energy electron excitations of the curved graphene sheet Σ are solutions of the massless Dirac equation on a 2+1 dimensional ultra-static metric on \Bbb R × Σ. 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.