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Convexity of reduced energy and mass angular momentum inequalities

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arxiv 1209.0019 v1 pith:7HREZH2C submitted 2012-08-31 math.DG gr-qc

Richard Schoen , Xin Zhou This is my paper · ORCID
classification math.DGgr-qc
keywords citedataextremeangularconvexityenergygivekerr-newman
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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.

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Cited by 1 Pith paper

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  1. On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes

    gr-qc 2025-07 conditional novelty 4.0 of 10

    For subextremal Kerr spacetimes, the paper constructs a positive-definite, conserved Hamiltonian energy for axially symmetric linear perturbations, indicating a form of linear stability within this symmetry class.

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