Observer-dependent optical properties of stationary axisymmetric spacetimes

TL;DR

This paper explores how the optical properties of stationary axisymmetric spacetimes depend on the observer's frame, introducing observer-dependent optical path and refraction index, with explicit examples in black hole spacetimes.

Contribution

It develops a framework for observer-dependent optical properties in stationary spacetimes, extending the concept of optical path and refraction index for null particles.

Findings

Observer-dependent optical path and refraction index are explicitly derived.

Explicit examples are provided for null orbits in black hole spacetimes.

The relation between relative standard time and coordinate time is clarified.

Abstract

The world lines of null particles admit arbitrary parametrizations. In the presence of a family of observers one may introduce along a null world line an extension of the so-called Cattaneo's relative standard time parameter (valid for massive particles) which plays a special role. Another possibility is to use the coordinate time itself as a parameter. The relation between relative standard time and coordinate time allows for the introduction of an observer-dependent optical path and associated refraction index. Both these quantities are studied here working out explicit examples concerning familiar null orbits and observers in black hole spacetimes.