Exact analytic photon escape cones and silhouettes for extremal Kerr

TL;DR

This paper provides exact analytic formulas for photon escape cones and silhouettes around extremal Kerr black holes, enabling precise understanding of black hole shadows without numerical approximations.

Contribution

It introduces fully explicit analytic expressions for photon escape cones and silhouettes in extremal Kerr spacetime, unlike the numerical or perturbative methods used for non-extremal cases.

Findings

Exact analytic formulas for photon escape cones.

Explicit silhouettes of extremal Kerr black holes.

Analytic approach simplifies understanding of black hole shadows.

Abstract

We exhibit exact analytic, fully explicit, photon escape cones and related silhouettes ("shadows") at arbitrary distance from the extremal Kerr black hole. In contrast to the situation for non-extremal Kerr, where one typically has to resort to either numerical and/or perturbative investigations, the situation for extremal Kerr is amenable to direct analytic investigation.