Lower bound on the radii of black-hole photonspheres

Abstract

The existence of closed null circular geodesics around black holes is one of the most intriguing predictions of general relativity. It has recently been conjectured that the radii of black-hole photonspheres are bounded from below by the simple relation $r_{\text{ph}}\ge \frac{3}{2}{r}_{\text{H}}$, where $r_{\text{H}}$ is the radius of the outer black-hole horizon. We here prove the validity of this conjecture for spherically symmetric hairy black-hole configurations whose radial pressure function $P\equiv |r^{3}p|$ decreases monotonically.

8 pages

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• Radii of spherical photon orbits around Kerr-Newman black holes
• Bound on photon circular orbits in general relativity and beyond
• Bounds for Lyapunov exponent of circular light orbits in black holes
• Circular light orbits of a general, static, and spherical symmetrical wormhole with $Z_2$ symmetry
• Analyzing the Influence of Geometrical Deformation on Photon Sphere and Shadow Radius: A New Analytical Approach -Stationary, and Axisymmetric Spacetime
• New look at AdS black holes with conformal scalar hair
• Gravitational Black Hole Shadow Spectroscopy
• 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
• Bounds on the photon sphere radius for spherically symmetric black holes in n-dimensional Einstein gravity
• Images and photon regions of continuous photon sphere spacetime