Compactness of relativistic charged spheres

Abstract

The Buchdahl bound states that the radius to mass ratio of a star is equal or greater than 9/4, on the assumption that the star is made of a perfect fluid, the density is a nonincreasing function of the radius and the exterior is the Schwarzschild solution. The bound is saturated by the infinite central pressure Schwarzschild interior solution. A generalization of this bound to electrically charged stars has been given by Andréasson. This Buchdahl-Andréasson bound is found through the assumption that the radial pressure plus twice the tangential pressure of the matter is less than the energy density. For zero electric charge one recovers the Buchdahl bound. A class of configurations that saturate the electrically charged Buchdahl-Andréasson bound are electrically charged shells. Another class of configurations is found here. Indeed, Guilfoyle's electrically charged stars which have a very stiff equation of state, the Cooperstock-de la Cruz-Florides equation of state, also saturate the bound. When the electric charge is zero Guilfoyle's stars reduce to the Schwarzschild incompressible stars.