Gravitational equilibria of self-interacting charged scalar fields

I present the static spherically symmetric gravitational equilibria of scalar fields coupled to a U(1) gauge field and with a possible λ/4(φ *φ)2 self-interaction. These configurations are obtained by solving numerically the coupled system of Einstein-Maxwell-Klein-Gordon equations for non-singular and asymptotically flat solutions. Static solutions only exist for values of the gauge coupling constant such that e2/4π ≤ GNm2, where m is the mass of the scalar particle. The maximum mass of the Bose star increases with increasing value of the gauge coupling constant. I discuss also the dynamical stability of the equilibrium configurations, for which I derive the pulsation equation, which governs the time evolution of the infinitesimal radial oscillations, as well as a variational principle for its eigenvalues. The equilibrium configurations with a central density bigger than ρcrit, corresponding to the critical mass, are dynamically unstable. (orig.)