https://doi.org/10.1140/epjc/s10052-025-14727-4
Letter
The existence and upper bound for stable photon spheres in static spherically symmetric black holes
College of Physics, Chengdu University of Technology, 610059, Chengdu, Sichuan, China
Received:
9
July
2025
Accepted:
4
September
2025
Published online:
13
September
2025
In this work, we establish the existence conditions and a universal upper bound on the radius of stable photon spheres (SPS) outside the event horizons of static, spherically symmetric, asymptotically flat black holes surrounded by matter fields. We prove that stable photon spheres exist if the external matter satisfies specific conditions. Furthermore, under the additional assumption of a monotonically decreasing mass-radius ratio 
outside the horizon, we derive a strict upper bound on the radius 
of any stable photon sphere: 
, where M is the asymptotic mass of the black hole. This bound is independent of specific black hole solutions and broadly applies to hairy black holes and other configurations with external matter fields meeting the stated energy conditions. Our results resolve fundamental questions regarding the existence and spatial constraints on stable photon orbits, with implications for gravitational lensing, accretion disk dynamics (e.g., the Aschenbach effect), and black hole shadow observations.
© The Author(s) 2025
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