Proof of a dain inequality with charge

Abstract

We prove an upper bound for angular momentum and charge in terms of the mass for electro-vacuum asymptotically flat axisymmetric initial data sets with simply connected orbit space. This completes the work started in (Chruściel and Costa 2009 Class. Quantum Grav. 26 235013 (arXiv:gr-qc/0909.5625)) where this charged Dain inequality was first presented but where the proof of the main result, based on the methods of Chruściel et al (Ann. Phys. 2008 323 2591–613 (arXiv:gr-qc/0712.4064v2)), was only sketched. Here we present a complete proof while simplifying the methods suggested by Chruściel and Costa (2009 Class. Quantum Grav. 26 235013 (arXiv:gr-qc/0909.5625)).