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Title:
Null Geometry and the Penrose Conjecture
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Abstract:
In the first half of the talk, we introduce a new quasi-local mass with interesting properties along null flows off of a 2-sphere in spacetime or, equivalently, foliations of a null cone. We also show how certain convexity assumptions on the null cone allows for a proof of the Penrose Conjecture. On the Black Hole Horizon, we find that this convexity assumption becomes sharp; therefore, the second half of the talk will explore the existence of a class of Black Hole Horizons satisfying the convexity assumptions even up to a small perturbation. A consequence of which, building upon the work of S. Alexakis, is that the Schwarzschild Null Cone--the case of equality for the Penrose Conjecture--is critical.
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