A geometrical approach to gravitational lensing magnification

TL;DR

This paper extends the concept of gravitational lensing magnification to Lorentzian spacetimes, providing a geometric interpretation using the van Vleck determinant and exponential map, thus broadening theoretical understanding.

Contribution

It introduces a geometric framework for gravitational lensing magnification in Lorentzian spacetimes, linking it to the van Vleck determinant and exponential map.

Findings

Generalized lensing magnification definition for Lorentzian spacetimes

Established geometric interpretation using van Vleck determinant

Provides a foundation for further theoretical developments

Abstract

The standard definition of gravitational lensing magnification is generalized to Lorentzian spacetimes, and it is shown how it can be interpreted geometrically in terms of the van Vleck determinant and the exponential map. This is joint work with Amir B. Aazami (Kavli IPMU, University of Tokyo).