Stationary Metrics and Optical Zermelo-Randers-Finsler Geometry

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dc.creatorGibbons, G. W.
dc.creatorHerdeiro, C. A. R.
dc.creatorWarnick, C. M.
dc.creatorWerner, M. C.
dc.date2008-11-18
dc.date.accessioned2026-07-07T13:11:10Z
dc.date.available2026-07-07T13:11:10Z
dc.descriptionWe consider a triality between the Zermelo navigation problem, the geodesic flow on a Finslerian geometry of Randers type, and spacetimes in one dimension higher admitting a timelike conformal Killing vector field. From the latter viewpoint, the data of the Zermelo problem are encoded in a (conformally) Painleve-Gullstrand form of the spacetime metric, whereas the data of the Randers problem are encoded in a stationary generalisation of the usual optical metric. We discuss how the spacetime viewpoint gives a simple and physical perspective on various issues, including how Finsler geometries with constant flag curvature always map to conformally flat spacetimes and that the Finsler condition maps to either a causality condition or it breaks down at an ergo-surface in the spacetime picture. The gauge equivalence in this network of relations is considered as well as the connection to analogue models and the viewpoint of magnetic flows. We provide a variety of examples.
dc.description37 pages, 6 figures
dc.identifierhttps://arxiv.org/abs/0811.2877
dc.identifierhttp://arxiv.org/abs/0811.2877
dc.identifierPhys.Rev.D79:044022,2009
dc.identifierdoi:10.1103/PhysRevD.79.044022
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/229203
dc.subjectGeneral Relativity and Quantum Cosmology
dc.subjectHigh Energy Physics - Theory
dc.subjectDifferential Geometry
dc.titleStationary Metrics and Optical Zermelo-Randers-Finsler Geometry
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