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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 the outward direction are positive in… Click to show full 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 the outward direction are positive in a 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 a $$t=\text{const.}$$ slice of the Schwarzschild spacetime.
Journal Title: Progress of Theoretical and Experimental Physics
Year Published: 2017
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