On uniqueness of static spacetimes with non-trivial conformal scalar field

Understand

We discuss the uniqueness of the static spacetimes with non-trivial conformal scalar field.

• Then, we can show that the spacetime is unique to be the Bocharova-Bronnikov-Melnikov-Bekenstein solution outside the surface composed of the unstable circular orbit of photon(photon surface).
• In addition, we see that multi-photon surfaces having the same scalar field values do not exist.