# Completing characterization of photon orbits in Kerr and Kerr-Newman metrics

## TL;DR

This paper introduces a comprehensive optical framework for understanding photon orbits in Kerr and Kerr-Newman spacetimes, classifying regions based on photon trapping and escape properties without solving geodesic equations.

## Contribution

It defines new regions like PTTS and PTTR to complete the photon orbit characterization in Kerr-like spacetimes, extending previous concepts and providing a novel optical description.

## Key findings

- Four distinct optical types identified in Kerr-Newman spacetimes.
- Extended Synge analysis to stationary spacetimes for photon escape.
- Density graphs illustrating photon escape regions.

## Abstract

Recently, several new characteristics have been introduced to describe null geodesic structure of stationary spacetimes, such as photon regions (PR) and transversely trapping surfaces (TTS). The former are three-dimensional domains confining the spherical photon orbits, while the latter are closed two-surface of spherical topology which fill other regions called TTR. It is argued that in generic stationary axisymmetric spacetime it is natural to consider also the non-closed TTSs of the geometry of spherical cups, satisfying the same conditions ("partial" TTS or PTTS), which fill the three-dimensional regions, PTTR. We then show that PR, TTR and PTTR together with the corresponding anti-trapping regions constitute the complete set of regions filling the entire three-space (where timelike surfaces are defined) of Kerr-like spacetimes. This construction provides a novel optical description of such spacetimes without recurring to explicit solution of the geodesic equations. Applying this analysis to Kerr-Newman metrics (including the overspinning ones) we reveal four different optical types for different sets of the rotation and charge parameters. To illustrate their properties we extend Synge analysis of photon escape in the Schwarzschild metric to stationary spacetimes and construct density graphs describing escape of photons from all the above regions.