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Area bound for a surface in a strong gravity region
- Source :
- Prog. Theor. Exp. Phys. (2017) 033E01
- Publication Year :
- 2017
-
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.<br />Comment: 5 pages, a reference added, minor changes, accepted for publication in PTEP
Details
- Database :
- arXiv
- Journal :
- Prog. Theor. Exp. Phys. (2017) 033E01
- Publication Type :
- Report
- Accession number :
- edsarx.1701.00564
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1093/ptep/ptx022