Gravity and Light: The Mathematics of Gravitational Lensing скачать в хорошем качестве

Gravity and Light: The Mathematics of Gravitational Lensing

The deflection of light due to gravity is one of the central predictions of Einstein’s general relativity, and can be used to test the theory and its modifications. Various mathematical frameworks exist to study this phenomenon, from the thin lens approximation used in astronomy to the full treatment in terms of null geodesics of Lorentzian spacetimes and optical geometry. In this talk, I will give an introduction to the geometrical and topological properties of gravitational lensing, covering classical results such as the odd number theorem as well as some of my own research. This includes magnification invariants and Lefschetz fixed point theory; the Gauss-Bonnet method in the Riemannian optical geometry of static spacetimes and the Finslerian optical geometry of stationary spacetimes; and recent results on the isoperimetric problem in Riemannian optical geometry. Given the current interest in modified theories of gravity, I will also mention a new approach called constructive gravity.