Convexity of Reduced Energy and Mass Angular Momentum Inequalities

Abstract

In this paper, we extend the work in Chruściel and Costa (Class. Quant. Grav. 26:235013, 2009), Chruściel et al. (Ann. Phy. 323:2591-2613, 2008), Costa (J. Math. Theor. 43:285202, 2010), Dain (J. Diff. Geom. 79:33-67, 2008). We weaken the asymptotic conditions on the second fundamental form, and we also give an L6-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. © 2013 Springer Basel.