Stability of boson stars

Boson stars are gravitationally bound, spherically symmetric equilibrium configurations of cold, free, or interacting complex scalar fields φ. As these equilibrium configurations naturally present local anisotropy, it is sensible to expect departures from the well-known stability criteria for fluid stars. With this in mind, I investigate the dynamical instability of boson stars against charge-conserving, small radial perturbations. Following the method developed by Chandrasekhar, a variational base for determining the eigenfrequencies of the perturbations is found. This approach allows one to find numerically an upper bound for the central density where dynamical instability occurs. As applications of the formalism, I study the stability of equilibrium configurations obtained both for the free and for the self-interacting [with V(φ)=(λ/4)‖φ${\Vert }^4$] massive scalar field φ. Instabilities are found to occur not for the critical central density as in fluid stars but for central densities considerably higher. The departure from the results for fluid stars is sensitive to the coupling λ; the higher the value of λ, the more the stability properties of boson stars approach those of a fluid star. These results are linked to the fractional anisotropy at the radius of the configuration.