Stationary Metrics and Optical Zermelo-Randers-Finsler Geometry
By G. W. Gibbons, Carlos A. R. Herdeiro, C. Warnick, M. Werner. 2008
137 citations recorded by the source corpus.
We consider a triality between the Zermelo navigation problem, the geodesic flow on a Fins- lerian 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 is- sues, 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 rela- tions is considered as well as the connection to analogue models and the viewpoint of magnetic flows. We provide a variety of examples.
Subfields: Astronomy and Astrophysics, Biophysics
View Paper: https://www.semanticscholar.org/paper/e7cdaf8d3254f97222b50895cb2054325b0dfe00
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In Astronomy and Astrophysics
- Charles Marteau
- Steen Markvorsen
- K. Siampos
- Luca Ciambelli
- A. Petkou
- P. Petropoulos
- M. Werner
- A. Ovgun
In Biophysics
Citations in the corpus
- A Finsler geodesic spray paradigm for wildfire spread modelling (2016, methodology): “We refer to [48, 49, 50, 47, 51, 4, 52, 53, 54, 8, 55, 56, 57, 5, 58, 59, 60] for details on Randers spaces and on the Zermelo navigation problem.”
- Covariant Galilean versus Carrollian hydrodynamics from relativistic fluids (2018, background): “6 See [15] for an interesting discussion on Zermelo versus Randers–Papapetrou forms.”
- Gravitational lensing in the Kerr-Randers optical geometry (2012, background): “A more detailed discussion of this and further examples can be found in [8].”