"Penrose inequality" for photon surface
Penrose inequality shows the maximum area of black hole horizon. Equality holds iff spacetime metric is Schwarzschild solution. We do a similar discussion for “photon surface”, not for horizon. We introduce a concept showing the strong gravity region “loosely trapped surface”. We proof that the area $A_0$ of loosely trapped surface satisfies the inequality $A_0 \le 4\pi (3Gm)^2$, where $m$ is ADM mass of the spacetime. The equality holds iff the spacetime metric is Schwarzschild solution, and then the loosely trapped surface is the photon sphere of Schwarzschild solution.