Penrose Conjecture
More generally, Penrose conjectured that an inequality as above should hold for spacelike submanifolds of spacetimes that are not necessarily time-symmetric. In this case, nonnegative scalar curvature is replaced with the dominant energy condition, and one possibility is to replace the minimal surface condition with an apparent horizon condition. Proving such an inequality remains an open problem in general relativity, called the Penrose Conjecture.
Read more about this topic: Riemannian Penrose Inequality
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—Mark Twain [Samuel Langhorne Clemens] (1835–1910)