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

Abstract

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

12 pages

References in corpus (5)

• Mass and angular-momentum inequalities for axi-symmetric initial data sets I. Positivity of mass
• On the shape of bodies in General Relativistic regimes
• Brown-York mass and the hoop conjecture in non-spherical massive systems
• Inequalities Between Size and Charge for Bodies and the Existence of Black Holes Due to Concentration of Charge
• The inequality between size and charge in spherical symmetry

Cited by in corpus (6)

• Self-gravitating magnetised tori around black holes in general relativity
• Bekenstein Bounds, Penrose Inequalities, and Black Hole Formation
• Toroidal marginally outer trapped surfaces in closed Friedmann-Lemaitre-Robertson-Walker spacetimes: Stability and isoperimetric inequalities
• Size, angular momentum and mass for objects
• Self-gravitating perfect-fluid tori around black holes: Bifurcations, ergoregions, and geometrical properties
• Two mass conjectures on axially symmetric black hole--disk systems