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Main Authors: Song, Yong, Fu, Jiaqi, Cen, Yiting
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2508.19823
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author Song, Yong
Fu, Jiaqi
Cen, Yiting
author_facet Song, Yong
Fu, Jiaqi
Cen, Yiting
contents 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 $m(r)/r^3$ outside the horizon, we derive a strict upper bound on the radius $r_{\mathrm{sps}}$ of any stable photon sphere: $r_{\mathrm{sps}}<6M$, 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.
format Preprint
id arxiv_https___arxiv_org_abs_2508_19823
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle The existence and upper bound for stable photon spheres in static spherically symmetric black holes
Song, Yong
Fu, Jiaqi
Cen, Yiting
General Relativity and Quantum Cosmology
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 $m(r)/r^3$ outside the horizon, we derive a strict upper bound on the radius $r_{\mathrm{sps}}$ of any stable photon sphere: $r_{\mathrm{sps}}<6M$, 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.
title The existence and upper bound for stable photon spheres in static spherically symmetric black holes
topic General Relativity and Quantum Cosmology
url https://arxiv.org/abs/2508.19823