  We consider a class of static and spherically symmetric black hole geometries
endowed with a photon sphere. On the one hand, we show that close to the photon
sphere, a massless scalar field theory exhibits a simple dynamical
$SL(2,\mathbb{R})$ algebraic structure which allows to recover the discrete
spectrum of the weakly damped quasinormal frequencies in the eikonal
approximation, and the associated quasinormal modes from the algebra
representations. On the other hand, we consider the non-radial motion of a
free-falling test particle, in the equatorial plane, from spatial infinity to
the black hole. In the ultrarelativistic limit, we show that the photon sphere
acts as an effective Rindler horizon for the geodesic motion of the test
particle in the $(t, r)$-plane, with an associated Unruh temperature $Tc =
\hbar\Lambda_c/2\pi k_B$, where $\Lambda_c$ is the Lyapunov exponent that
characterizes the unstable circular motions of massless particles on the photon
sphere. The photon sphere then appears as a location where the thermal bound on
chaos for quantum systems with a large number of degrees of freedom, in the
form conjectured a few years ago by Maldacena et al., is saturated. The study
developed in this paper could hopefully shed a new light on the gravity/CFT
correspondence, particularly in asymptotically flat spacetimes, in which the
photon sphere may also be considered as a holographic screen.
