Inequality between size and angular momentum for bodies

Abstract

A universal inequality that bounds the angular momentum of a body by the square of its size is presented and heuristic physical arguments are given to support it. We prove a version of this inequality, as consequence of Einstein equations, for the case of rotating axially symmetric, constant density, bodies. Finally, the physical relevance of this result is discussed.

Improvements in the heuristic arguments. 5 pages

References in corpus (4)

• Geometric inequalities for axially symmetric black holes
• A Reformulation of the Hoop Conjecture
• What is the Shape of a Black Hole?
• Some remarks on the size of bodies and black holes

Cited by in corpus (13)

• Geometrical inequalities bounding angular momentum and charges in General Relativity
• Geometric inequalities for black holes
• On the shape of bodies in General Relativistic regimes
• Bekenstein bounds and inequalities between size, charge, angular momentum and energy for bodies
• Rotating systems, universal features in dragging and anti-dragging effects, and bounds onto angular momentum
• Penrose-like inequality with angular momentum for minimal surfaces
• Inequalities Between Size and Charge for Bodies and the Existence of Black Holes Due to Concentration of Charge
• Size, angular momentum and mass for objects
• Inequalities Between Size, Mass, Angular Momentum, and Charge for Axisymmetric Bodies and the Formation of Trapped Surfaces
• Comments on Penrose inequality with angular momentum for outermost apparent horizons
• The inequality between size and charge in spherical symmetry
• Refined inequalities for loosely trapped surface/attractive gravity probe surface
• Existence of Black Holes Due to Concentration of Angular Momentum