Dynamical evolution of boson stars: Perturbing the ground state

This is the first paper in a series in which we study the dynamical evolution of self-gravitating complex scalar field configurations (boson stars) in numerical relativity. Boson stars have equilibrium configurations corresponding to different levels of excitation of the scalar fields (i.e., different numbers of nodes). In this paper we report on the dynamical evolution of the perturbed ground-state boson stars. The major results are the following. (i) Under finite perturbations (with possibly finite changes in the total mass $M$ and the particle number $N$), the ground-state configurations of a boson star consist of a stable branch and an unstable branch. The transition point corresponds to a critical mass of $M=0.633\left(\frac{M_{\mathrm{Planck}}^2}{m}\right)$, where $m$ is the mass of the scalar field, depending slightly on the type of perturbation considered. This extends the previous result obtained by other authors that there are two such branches under infinitesimal perturbations with fixed $M$ and $N$. (ii) The configurations on the stable branch, when perturbed, will oscillate, emit scalar field radiation with a characteristic frequency, and settle down into a new configuration with less mass and a larger radius than the initial perturbed configuration. The quasinormal frequency and the decay rate have been studied. The decay rate is an increasing function of the oscillation amplitude. (iii) The configurations on the unstable branch, when perturbed, either collapse to a black hole or migrate to and eventually settle down on the stable branch, depending on the type of perturbation. This behavior has been seen in initial configurations with both positive and negative binding energies. These results have implications on the actual existence and the formation of boson stars in an astrophysical environment.