P.d.e.'s which imply the Penrose conjecture

Details P.d.e.'s which imply the Penrose conjecture P.d.e.'s which imply the Penrose conjecture

2009-05-15

arxiv.org/abs/0905.2622v1

Mathematics

Differential Geometry

63 pages, 2 figures

Scientific paper

In this paper, we show how to reduce the Penrose conjecture to the known Riemannian Penrose inequality case whenever certain geometrically motivated systems of equations can be solved. Whether or not these special systems of equations have general existence theories is therefore an important open problem. The key tool in our method is the derivation of a new identity which we call the generalized Schoen-Yau identity, which is of independent interest. Using a generalized Jang equation, we propose canonical embeddings of Cauchy data into corresponding static spacetimes. In addition, our techniques suggest a more general Penrose conjecture and generalized notions of apparent horizons and trapped surfaces, which are also of independent interest.

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