Cuspy and fractured black hole shadows in a toy model with axisymmetry

TL;DR

This paper introduces a simplified axisymmetric black hole model with a dark matter shell to study complex shadow features like cusps and fractures, revealing rich photon orbit structures and novel shadow phenomena.

Contribution

It presents a minimal toy model demonstrating how cuspy and fractured black hole shadows can arise from fundamental photon orbit transitions in a simplified setting.

Findings

Discovery of two disconnected branches of unstable photon orbits

Observation of cuspy and fractured black hole shadows

Identification of incomplete Einstein ring arcs

Abstract

Cuspy shadow was first reported for hairy rotating black holes, whose metrics deviate significantly from the Kerr one. The non-smooth edge of the shadow is attributed to a transition between different branches of unstable but bounded orbits, known as the fundamental photon orbits, which end up at the light rings. In searching for a minimal theoretical setup to reproduce such a salient feature, in this work, we devise a toy model with axisymmetry, a slowly rotating Kerr black hole enveloped by a thin slowly rotating dark matter shell. Despite its simplicity, we show rich structures regarding fundamental photon orbits explicitly in such a system. We observe two disconnected branches of unstable spherical photon orbits, and the jump between them gives rise to a pair of cusps in the resultant black hole shadow. Besides the cuspy shadow, we explore other intriguing phenomena when the Maxwell construction cannot be established. We find that it is possible to have an incomplete arc of Einstein rings and a "fractured" shadow. The potential astrophysical significance of the corresponding findings is addressed.