Area bound for a surface in a strong gravity region
  For asymptotically flat spacetimes, using the inverse mean curvature flow, we
show that any compact $2$-surface, $S_0$, whose mean curvature and its
derivative for outward direction are positive in spacelike hypersurface with
non-negative Ricci scalar satisfies the inequality $A_0 \leq 4 \pi (3Gm)^2$,
where $A_0$ is the area of $S_0$ and $m$ is the total mass. The upper bound is
realized when $S_0$ is the photon sphere in a hypersurface isometric to
$t=$const. slice of the Schwarzschild spacetime.
