标题： 坍塌的壳与黑洞的等周不等式 显示英文标题

标题： Collapsing Shells and the Isoperimetric Inequality for Black Holes

摘要： 近期Trudinger关于非凸体的等周不等式的结果被应用于光壳引力塌缩形成黑洞的问题。利用闵可夫斯基时空中共维数为二的曲面的一些积分恒等式，证明了视界面积$A$在质量$M$的条件下由$16 \pi G^2 M^2$给出上界，这与宇宙监督猜想一致。这些结果在四维以及更高维度时成立。 显示英文摘要

摘要： Recent results of Trudinger on Isoperimetric Inequalities for non-convex bodies are applied to the gravitational collapse of a lightlike shell of matter to form a black hole. Using some integral identities for co-dimension two surfaces in Minkowski spacetime, the area $A$ of the apparent horizon is shown to be bounded above in terms of the mass $M$ by the $16 \pi G^2 M^2$, which is consistent with the Cosmic Censorship Hypothesis. The results hold in four spacetime dimensions and above.