A jang equation approach to the penrose inequality

Journal Article (Journal Article)

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 dominant 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.

Full Text

Duke Authors

Cited Authors

  • Bray, HL; Khuri, MA

Published Date

  • June 1, 2010

Published In

Volume / Issue

  • 27 / 2

Start / End Page

  • 741 - 766

International Standard Serial Number (ISSN)

  • 1078-0947

Digital Object Identifier (DOI)

  • 10.3934/dcds.2010.27.741

Citation Source

  • Scopus