Stability of null orbits on photon spheres and photon surfaces

Understand

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.