On charged boson stars

We study static, spherically symmetric, self-gravitating systems minimally coupled to a scalar field with U(1) gauge symmetry: charged boson stars. We find numerical solutions to the EinsteinMaxwell equations coupled to the relativistic Klein-Gordon equation. It is shown that bound stable configurations exist only for values of the coupling constant less than or equal to a certain critical value. The metric coefficients and the relevant physical quantities such as the total mass and charge, turn out to be in general bound functions of the radial coordinate, reaching their maximum values at a critical value of the scalar field at the origin. We discuss the stability problem both from the quantitative and qualitative point of view. Taking properly into account the electromagnetic contribution to the total mass, the stability issue is faced also following an indication of the binding energy per particle, verifying then the existence of configurations having positive binding energy: objects apparently bound can be unstable against small perturbations, in full analogy with what observed in the mass-radius relation of neutron stars.