Publications (3)11.82 Total impact
 [Show abstract] [Hide abstract]
ABSTRACT: We 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) PainleveGullstrand 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 ergosurface 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. Comment: 37 pages, 6 figuresPhysical Review D 11/2008; 79(4):044022. · 4.69 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We interpret the well known fact that the equations for light rays in the Kottler or Schwarzschildde Sitter metric are independent of the cosmological constant in terms of the projective equivalence of the optical metric for any value of \Lambda. We explain why this does not imply that lensing phenomena are independent of \Lambda. Motivated by this example, we find a large collection of oneparameter families of projectively equivalent metrics including both the Kottler optical geometry and the constant curvature metrics as special cases. Using standard constructions for geodesically equivalent metrics we find classical and quantum conserved quantities and relate these to known quantities.Classical and Quantum Gravity 09/2008; · 3.56 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: In this geometrical approach to gravitational lensing theory, we apply the GaussBonnet theorem to the optical metric of a lens, modelled as a static, spherically symmetric, perfect nonrelativistic fluid, in the weak deflection limit. We find that the focusing of the light rays emerges here as a topological effect, and we introduce a new method to calculate the deflection angle from the Gaussian curvature of the optical metric. As examples, the Schwarzschild lens, the Plummer sphere and the singular isothermal sphere are discussed within this framework.Classical and Quantum Gravity 08/2008; · 3.56 Impact Factor
Publication Stats
65  Citations  
11.82  Total Impact Points  
Top Journals
Institutions

2008

University of Cambridge
 Institute of Astronomy
Cambridge, England, United Kingdom
