# Covariant kinematics of light in media and a generalized Raychaudhuri equation

## TL;DR

This paper develops a covariant framework for analyzing light propagation in various media within curved spacetime, generalizing the Raychaudhuri equation to enhance understanding of optical systems and their relation to general relativity.

## Contribution

It introduces a covariant kinematic approach for light in media and extends the Raychaudhuri equation to media with varying refractive properties and spacetime characteristics.

## Key findings

- Derived covariant kinematics of light in media within curved spacetime
- Generalized Raychaudhuri equation for diverse media and spacetime types
- Potential applications in transformation optics and gravitational studies

## Abstract

There is ongoing interest in adopting various tools and ideas from general relativity for optical applications and the study of light propagation through natural or engineered media. Here, the covariant kinematics of light propagating through arbitrary dielectric media in curved space-times are derived, allowing for analysis and tracing of congruences of light through media that may smoothly vary in character between vacuum, positively refracting, and negatively refracting; or null, timelike, and spacelike with respect to the background metric. The kinematics are then used to generalize the Raychaudhuri equation -- an important tool in general relativity that describes the focus of a congruence. These results will be useful for the analysis of optical devices, particularly those designed using transformation optics, and serve as theoretical tools to study generalized concepts in general relativity.