Light rings in static and extremal black holes

Abstract

In this work we establish some results concerning the existence of external light rings in extremal black hole spacetimes through the Newman-Penrose formalism. Specifically, assuming conformal flatness, staticity and the null energy condition, we show that a sufficient condition for the existence of external light rings is $R<2K_G$, where $R$, the curvature scalar of the spacetime and $K_G$, the Gaussian curvature of a spacelike two-surface, are both evaluated at the outermost event horizon, which can be endowed with spherical, hyperbolic or planar geometry. Our results are valid for any metric gravity theory where photons follow null geodesics.

To be submitted to Phys. Rev. D

References in corpus (12)

• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• First M87 Event Horizon Telescope Results. VI. The Shadow and Mass of the Central Black Hole
• First M87 Event Horizon Telescope Results. V. Physical Origin of the Asymmetric Ring
• Stationary black holes and light rings
• Topological Charge and Black Hole Photon Spheres
• Upper bound on the radii of black-hole photonspheres
• Universal Properties of Light Rings for Stationary Axisymmetric Spacetimes
• Light rings of stationary spacetimes
• Geometric Approach to Circular Photon Orbits and Black Hole Shadows
• The spatial relation between the event horizon and trapping horizon
• Curvatures, Photon Spheres and Black Hole Shadows
• Photon surfaces in less symmetric spacetimes

Cited by in corpus (3)

• Rényi Topology of Charged-flat Black Hole: Hawking-Page and Van-der-Waals Phase Transitions
• The Existence and Distribution of Photon Spheres Near Spherically Symmetric Black Holes -- A Geometric Analysis
• A General Discussion on Photon Spheres in Different Categories of Spacetimes