  Stability of a photon sphere, or stability of circular null geodesics on the
sphere, plays a key role in its applications to astrophysics. For instance, an
unstable photon sphere is responsible for determining the size of a black hole
shadow, while a stable photon sphere is inferred to cause the instability of
spacetime due to the trapping of gravitational waves on the radius. A photon
surface is a geometrical structure first introduced by Claudel, Virbhadra and
Ellis as the generalization of a photon sphere. The surface does not require
any symmetry of spacetime and has its second fundamental form pure-trace. In
this paper, we define the stability of null geodesics on a photon surface. It
represents whether null geodesics perturbed from the photon surface are
attracted to or repelled from the photon surface. Then, we define a strictly
(un)stable photon surface as a photon surface on which all null geodesics are
(un)stable. We find that the stability is determined by Riemann curvature.
Furthermore, it is characterized by the normal derivative of the second
fundamental form. As a consequence, for example, a strictly unstable photon
surface requires nonvanishing Weyl curvature on it if the null energy condition
is satisfied.
