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

摘要

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 the other regions, called transversely trapping region (TTR). It is argued that in a generic stationary axisymmetric spacetime it is natural to consider also the nonclosed TTSs of the geometry of spherical cups, satisfying the same conditions locally ("partial" TTS or PTTS), which fill the three-dimensional regions, PTTR. We then show that PR, TTR and PTTR together with the corresponding antitrapping regions constitute the complete set of domains filling the entire Kerr-like spacetimes. This construction provides a novel optical description of such spacetimes which does not require explicit solution of 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 the Synge and Semerak analysis of photon escape to stationary spacetimes and construct density graphs describing escape of photons from all the above regions.