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A universal inequality that bounds the charge of a body by its size is presented, and is proven as a consequence of the Einstein equations in the context of initial data sets which satisfy an appropriate energy condition. We also present a general sufficient condition for the formation of black holes due to concentration of charge, and discuss the physical relevance of these results.
We present a general sufficient condition for the formation of black holes due to concentration of angular momentum. This is expressed in the form of a universal inequality, relating the size and angular momentum of bodies, and is proven in the conte
A universal geometric inequality for bodies relating energy, size, angular momentum, and charge is naturally implied by Bekensteins entropy bounds. We establi
We establish the conjectured area-angular momentum-charge inequality for stable apparent horizons in the presence of a positive cosmological constant, and show that it is saturated precisely for extreme Kerr-Newman-de Sitter horizons. As with previou
We construct transformations which take asymptotically AdS hyperbolic initial data into asymptotically flat initial data, and which preserve relevant physical quantities. This is used to derive geometric inequalities in the asymptotically AdS hyperbo
We report about the possibility for interacting Kerr sources to exist in two different states - black holes or naked singularities - both states characterized by the same masses and angular momenta. Another surprising discovery reported by us is that