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, |S₀|⁠, whose mean curvature and its derivative for the outward direction are positive in a spacelike hypersurface with non-negative Ricci scalar satisfies the inequality |A₀ \,≤\, 4π (3Gm)²|⁠, where |A₀| is the area of |S₀| and |m| is the total mass. The upper bound is realized when |S₀| is the photon sphere in a hypersurface isometric to a |t=const.| slice of the Schwarzschild spacetime.