Nonlinear Dynamics of Spinning Bosonic Stars: Formation and Stability

We perform numerical evolutions of the fully nonlinear Einstein (complex, massive) Klein-Gordon and Einstein (complex) Proca systems, to assess the formation and stability of spinning bosonic stars. In the scalar (vector) case these are known as boson (Proca) stars. Firstly, we consider the formation scenario. Starting with constraint-obeying initial data, describing a dilute, axisymmetric cloud of spinning scalar or Proca field, gravitational collapse toward a spinning star occurs, via gravitational cooling. In the scalar case the formation is transient, even for a nonperturbed initial cloud; a nonaxisymmetric instability always develops ejecting all the angular momentum from the scalar star. In the Proca case, by contrast, no instability is observed and the evolutions are compatible with the formation of a spinning Proca star. Secondly, we address the stability of an existing star, a stationary solution of the field equations. In the scalar case, a nonaxisymmetric perturbation develops, collapsing the star to a spinning black hole. No such instability is found in the Proca case, where the star survives large amplitude perturbations; moreover, some excited Proca stars decay to, and remain as, fundamental states. Our analysis suggests bosonic stars have different stability properties in the scalar (vector) case, which we tentatively relate to its toroidal (spheroidal) morphology. A parallelism with instabilities of spinning fluid stars is briefly discussed.

Figure 1

Surfaces of constant energy density for illustrative SBSs. Left: Scalar configuration $2_S$. Right: Vector configuration $1_P$. The toroidal vs spheroidal nature is clear.

Figure 2

Time evolution of an equatorial cut of ${\rho }_E$ (blue or green) and ${\rho }_J$ (orange) in the formation scenario of a scalar (left-hand side) or a vector (right-hand side) SBS.

Figure 3

Time evolution of a scalar SBS, model $2_S$. Six sequential snapshots of ${\rho }_E$ (top panels). Time runs left to right, first to second row. Total scalar field energy and apparent horizon mass (main panel) and lapse function (inset).

Figure 4

Time evolution of vector SBSs. Equatorial cut of ${\rho }_E$ (blue) and ${\rho }_J$ (orange) for the FF model $1_P$ with a perturbation (left-hand side) and the excited model $3_P$ (right-hand side).