Looking through the Kerr disk

TL;DR

This paper analyzes null geodesics in Kerr spacetime connecting different asymptotic regions, revealing unique photon trajectories, their properties, and visual effects, with implications for understanding black hole and white hole geometries.

Contribution

It provides a detailed analytical and numerical study of connecting null geodesics in Kerr spacetime, extending previous models and exploring their visual signatures.

Findings

Identification of the inner throat region with no radial turning points.

Analytical and numerical solutions for geodesic equations in Kerr spacetime.

Simulated images showing strong distortion and inversion effects.

Abstract

We study null geodesics that connect the two asymptotically flat regions of the maximally extended Kerr spacetime. These vortical geodesics traverse both horizons and pass through the ring singularity, linking the positive-$r$ exterior to the negative-$r$ asymptotic side. Using impact parameters, we identify a closed subset of parameter space, the inner throat, where the radial potential has no real roots, and photons exhibit no radial turning points. In this region, at most two constant-latitude geodesics exist, one of which is aligned with the principal null direction. We also identify the forbidden polar-angle band that limits the range of geodesics reaching an asymptotic observer. We solve the geodesic equations analytically and numerically in Eddington-Finkelstein-like coordinates, obtaining mutually consistent results that correct and extend previously available formulae. The resulting trajectories are used to construct simulated views for an observer in the negative-$r$ domain, revealing strong image distortion and inversion, with possible implications for analogous white-hole configurations.