Convexity of reduced energy and mass angular momentum inequalities

TL;DR

This paper proves convexity of a renormalized energy functional under weaker conditions and establishes a strict mass-angular momentum-charge inequality for axisymmetric Einstein/Maxwell data, extending previous results.

Contribution

It introduces a new convexity proof for the energy functional with relaxed asymptotic conditions and demonstrates a strict inequality for a broader class of data.

Findings

Convexity of the renormalized Dirichlet energy under non-positive curvature.

An $L^{6}$-norm bound for differences between general and extreme Kerr data.

First proof of strict mass/angular momentum/charge inequality beyond extreme Kerr-Newman.

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.