Optical Geometry and the Magnetoelectric Effect

Abstract:
Optical geometry is a spatial formalism for light propagation in
Lorentzian spacetimes. This provides a useful framework for
gravitational lensing which is geometrically interesting and
includes applications of non-Lorentzian geometries. In this talk,
I will first consider Riemannian optical geometry, and review basic
results as well as recent work using the Gauss-Bonnet method
and curve-shortening flow. In particular, the first isoperimetric
inequality in this context will be presented. Then I will discuss
Finslerian optical geometry of stationary spacetimes, including
the Kerr-Randers structure and extensions of the Gauss-Bonnet
method. I will highlight the connection with Jacobi-Maupertuis
metrics and the magnetoelectric effect. Finally, a framework for
optics in non-metric spacetimes will be sketched briefly.