Shadow Formation Conditions Beyond the Kerr Black Hole Paradigm

Abstract

A compact object illuminated by background radiation produces a dark silhouette. The edge of the silhouette or shadow (alternatively, the apparent boundary or the critical curve) is commonly determined by the presence of the photon sphere (or photon shell in the case of rotating spacetime), corresponding to the maximum of the effective potential for null geodesics. While this statement stands true for Kerr black holes, here we remark that the apparent boundary (as defined by Bardeen) forms under a more general condition. We demonstrate that a shadow forms if the effective potential of null geodesics has a positive finite upper bound and includes a region where photons are trapped or scattered. Our framework extends beyond conventional solutions, including but not limited to naked singularities. Furthermore, we clarify the difference between the apparent boundary of a dark shadow and the bright ring on the screen of a distant observer. These results provide a unified theoretical basis for interpreting observations from the Event Horizon Telescope (EHT) and guiding future efforts towards extreme-resolution observations of compact objects.

References in corpus (14)

• Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A${}^{\ast }$
• Naked Singularities in Spherically Symmetric Inhomogeneous Tolman-Bondi Dust Cloud Collapse
• Shadows of spherically symmetric black holes and naked singularities
• Equilibrium configurations from gravitational collapse
• Shadow of a Naked Singularity without Photon Sphere
• Shadow of nulllike and timelike naked singularities without photon spheres
• Strong curvature naked singularities in spherically symmetric perfect fluid collapse
• Gravitational collapse of an isentropic perfect fluid with a linear equation of state
• On the global visibility of singularity in quasi-spherical collapse
• Global visibility of a strong curvature singularity in nonmarginally bound dust collapse
• Globally visible singularity in an astrophysical setup
• Causal Structure of Singularity in non-spherical Gravitational Collapse
• Imaging ultra-compact objects with radiatively inefficient accretion flows
• On the global visibility of a singularity in spherically symmetric gravitational collapse