Charged boson stars

We study time-independent, 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 Einstein-Maxwell 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 from both the quantitative and qualitative point of view. We take into account the electromagnetic contribution to the total mass and investigate the stability issue considering the binding energy per particle. We verify the existence of configurations with positive binding energy in which objects that are apparently bound can be unstable against small perturbations, in full analogy with the effect observed in the mass-radius relation of neutron stars.

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