Photon region boundary for stationary axisymmetric black holes

Abstract

The black hole shadow is fundamentally connected to the structure of light rings and the photon region in the background geometry. We investigate the photon region boundary in a generic asymptotically flat, stationary, axisymmetric black hole spacetime that admits spherical photon orbits (SPOs). Explicit expressions possessing real solutions are provided for the photon region's boundary purely in terms of the background metric functions, independent of the photon's parameters like energy or angular momentum, which are applicable to both separable and non-separable spacetimes. We further analyze its common features, including overlap with the ergoregion and rotation sense of SPOs. Additionally, light rings are identified at the extrema of the photon region boundary curves in the $(r,\theta )$ plane. Our approach is validated against a few exact black hole solutions. Implications are discussed.

v1: 25 pages, 9 figures; v2: 29 pages, 9 figures, references added, new discussion added; v3: 30 pages, 9 figures, Accepted for publication in PRD

References in corpus (23)

• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• First Sagittarius A* Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole in the Center of the Milky Way
• Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A${}^{\ast }$
• Calculating black hole shadows: Review of analytical studies
• Light ring stability in ultra-compact objects
• Light rings as observational evidence for event horizons: long-lived modes, ergoregions and nonlinear instabilities of ultracompact objects
• Photon Rings around Kerr and Kerr-like Black Holes
• Shadows of Einstein-dilaton-Gauss-Bonnet black holes
• Chaotic lensing around boson stars and Kerr black holes with scalar hair
• Fundamental photon orbits: black hole shadows and spacetime instabilities
• Shadow analysis for rotating black holes in the presence of plasma for an expanding universe
• Universal Properties of Light Rings for Stationary Axisymmetric Spacetimes
• Shadows of parametrized axially symmetric black holes allowing for separation of variables
• Cosmological constant corrections to the photon sphere and black hole shadow radii
• Light rings of stationary spacetimes
• Note on counterterms in asymptotically flat spacetimes
• Light rings and long-lived modes in quasi-black hole spacetimes
• Black Hole Shadows and Invariant Phase Space Structures
• Chaotic Shadows of Black Holes: A Short Review
• Spinning black holes with a separable Hamilton-Jacobi equation from a modified Newman-Janis algorithm
• Exact Formulas for Spherical Photon Orbits Around Kerr Black Holes
• Superentropic Black Hole Shadows in Arbitrary Dimensions
• On the nature of inner light-rings

Cited by in corpus (1)

• Gravitational lensing inside and outside of a marginally unstable photon sphere in a general, static, spherically symmetric, and asymptotically-flat spacetime in strong deflection limits