Convexity of reduced energy and mass angular momentum inequalities

Abstract

In this paper, we extend the work in \cite{D}\cite{ChrusLiWe}\cite{ChrusCo}\cite{Co}. We weaken the asymptotic conditions on the second fundamental form, and we also give an $L^6-$norm bound for the difference between general data and Extreme Kerr data or Extreme Kerr-Newman data by proving convexity of the renormalized Dirichlet energy when the target has non-positive curvature. In particular, we give the first proof of the strict mass/angular momentum/charge inequality for axisymmetric Einstein/Maxwell data which is not identical with the extreme Kerr-Newman solution.

27 pages

References in corpus (3)

• Mass and angular-momentum inequalities for axi-symmetric initial data sets. II. Angular-momentum
• Mass and angular-momentum inequalities for axi-symmetric initial data sets I. Positivity of mass
• A uniqueness theorem for degenerate Kerr-Newman black holes

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