标题： 束缚面和球对称几何中的彭罗斯不等式 显示英文标题

标题： Trapped surfaces and the Penrose inequality in spherically symmetric geometries

摘要： 我们证明，即使视界浸入物质中，Penrose 不等式对于球对称几何也是成立的。 物质场不需要静止。 唯一的限制是源在视界之外满足弱能量条件。 对视界内部的物质没有任何限制。 Penrose 不等式的证明给出了形成捕获面的新必要条件。 这种表述也可以调整以给出充分条件。 我们表明，Gibbons 为带电黑洞提出的 Penrose 不等式的修改形式在引力塌缩的早期阶段可以被打破。 这项研究完全基于广义相对论的初始数据表述。 显示英文摘要

摘要： We demonstrate that the Penrose inequality is valid for spherically symmetric geometries even when the horizon is immersed in matter. The matter field need not be at rest. The only restriction is that the source satisfies the weak energy condition outside the horizon. No restrictions are placed on the matter inside the horizon. The proof of the Penrose inequality gives a new necessary condition for the formation of trapped surfaces. This formulation can also be adapted to give a sufficient condition. We show that a modification of the Penrose inequality proposed by Gibbons for charged black holes can be broken in early stages of gravitational collapse. This investigation is based exclusively on the initial data formulation of General Relativity.