68 research outputs found
A Jang Equation Approach to the Penrose Inequality
We introduce a generalized version of the Jang equation, designed for the
general case of the Penrose Inequality in the setting of an asymptotically flat
space-like hypersurface of a spacetime satisfying the dominat energy condition.
The appropriate existence and regularity results are established in the special
case of spherically symmetric Cauchy data, and are applied to give a new proof
of the general Penrose Inequality for these data sets. When appropriately
coupled with an inverse mean curvature flow, analogous existence and regularity
results for the associated system of equations in the nonspherical setting
would yield a proof of the full Penrose Conjecture. Thus it remains as an
important and challenging open problem to determine whether this system does
indeed admit the desired solutions.Comment: 31 page
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