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We establish inequalities relating the size of a material body to its mass,angular momentum, and charge, within the context of axisymmetric initial datasets for the Einstein equations. These inequalities hold in general without theassumption of the maximal condition, and use a notion of size which is easilycomputable. Moreover, these results give rise to black hole existence criteriawhich are meaningful even in the time-symmetric case, and also include certainboundary effects.

Inequalities Between Size, Mass, Angular Momentum, and Charge for Axisymmetric Bodies and the Formation of Trapped Surfaces