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arXiv · 1701.00564

Area bound for a surface in a strong gravity region

Tetsuya Shiromizu·Yoshimune Tomikawa·Keisuke Izumi·Hirotaka Yoshino
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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 $A_0 \leq 4 \pi (3Gm)^2$, 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.

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Tetsuya Shiromizu, Yoshimune Tomikawa, Keisuke Izumi, Hirotaka Yoshino. 2017-01-03. Area bound for a surface in a strong gravity region. https://doi.org/10.1093/ptep/ptx022

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