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.

arXiv commentTo be submitted to Phys. Rev. D

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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