2026/07/31 by Filipe Cattete Alves, Rodrigo Maier
Physics and Astronomy · #gr-qc
arxiv created 2026/07/31 · arxiv updated 2026/08/04
We investigate the null geodesic structure, photon sphere dynamics, and high-energy particle collisions within a class of static, spherically symmetric hairy Horndeski black holes. Characterized by an invariant metric root at r = 2M and a scalar hair parameter Q, the spacetime maps onto four distinct geometric domains dictated by the surface gravity κ|2M. We derive exact analytical expressions for the photon sphere radius rph and its dynamic stability criterion, showing that external circular null orbits remain dynamically unstable across non-extremal regimes. Crucially, we prove that a stable photon sphere arises exclusively in the extremal configuration (Q = -2M), where it coincides precisely with the degenerate horizon (r = 2M). We argue that this horizon-bound stable photon orbit acts as an infinitely redshifted bound state for light and ultra-relativistic particles. Finally, we analyze the Bañados-Silk-West (BSW) effect for infalling timelike test particles, demonstrating that the center-of-mass energy Ecm for critical collisions diverges as Ecm ∝ (r - rh)-1/2 strictly at the extremal threshold Q = -2M.