The inequality between size and charge in spherical symmetry

Abstract

We prove that for a spherically symmetric charged body two times the radius is always strictly greater than the charge of the body. We also prove that this inequality is sharp. Finally, we discuss the physical implications of this geometrical inequality and present numerical examples that illustrate this theorem.

34 pages, 10 figures. Added references. New example in section 3.3

References in corpus (3)

• On the shape of bodies in General Relativistic regimes
• Bekenstein bounds and inequalities between size, charge, angular momentum and energy for bodies
• Inequalities Between Size and Charge for Bodies and the Existence of Black Holes Due to Concentration of Charge

Cited by in corpus (5)

• Geometrical inequalities bounding angular momentum and charges in General Relativity
• Bekenstein bounds and inequalities between size, charge, angular momentum and energy for bodies
• Size, angular momentum and mass for objects
• Inequalities Between Size, Mass, Angular Momentum, and Charge for Axisymmetric Bodies and the Formation of Trapped Surfaces
• Geometric inequalities in spherically symmetric spacetimes