Area bound for a surface in a strong gravity region

Abstract

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 $A_0\le 4\pi (3Gm{)}^2$, 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.

5 pages, a reference added, minor changes, accepted for publication in PTEP

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