First-order perturbative approach to charged boson stars

As it is known by now, the boson stars are gravitationally bound, both globally U(1) and spherically symmetric, compact equilibrium configurations of cold complex scalar fields. The aim of the present Letter is to study the (SO(3,1)xU(1))-gauged minimally coupled charged spinless field to a spherically symmetric spacetime and to analytically derive the first-order approximating solutions to the system of Klein-Gordon-Maxwell-Einstein equations. The instabilities we study could lead to the formation of boson stars from an initially smooth state. The corresponding (analytical) formulae for the charge, mass and radius of the boson stars can accommodate a wide range of numerical estimations, by tuning the model parameters