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Annales Henri Poincaré

, Volume 16, Issue 3, pp 841–896 | Cite as

Deformations of Axially Symmetric Initial Data and the Mass-Angular Momentum Inequality

  • Ye Sle Cha
  • Marcus A. KhuriEmail author
Article

Abstract

We show how to reduce the general formulation of the mass-angular momentum inequality, for axisymmetric initial data of the Einstein equations, to the known maximal case whenever a geometrically motivated system of equations admits a solution. This procedure is based on a certain deformation of the initial data which preserves the relevant geometry, while achieving the maximal condition and its implied inequality (in a weak sense) for the scalar curvature; this answers a question posed by R. Schoen. The primary equation involved, bears a strong resemblance to the Jang-type equations studied in the context of the positive mass theorem and the Penrose inequality. Each equation in the system is analyzed in detail individually, and it is shown that appropriate existence/uniqueness results hold with the solution satisfying desired asymptotics. Lastly, it is shown that the same reduction argument applies to the basic inequality yielding a lower bound for the area of black holes in terms of mass and angular momentum.

Keywords

Black Hole Scalar Curvature Dominant Energy Condition Kerr Spacetime Maximal Case 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Basel 2014

Authors and Affiliations

  1. 1.Department of MathematicsStony Brook UniversityStony BrookUSA

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