Boson stars driven to the brink of black hole formation

Abstract

We present a study of black hole threshold phenomena for a self-gravitating, massive complex scalar field in spherical symmetry. We construct Type I critical solutions dynamically by tuning a one-parameter family of initial data composed of a boson star and a massless real scalar field. The real field is used to perturb the boson star via a gravitational interaction which results in a {\em significant} transfer of energy. The resulting critical solutions, which show great similarity with unstable boson stars, persist for a finite time before dispersing or forming a black hole. We extend the stability analysis of Gleiser and Watkins [Nucl. Phys. B319, 733 (1989)], providing a method for calculating the radial dependence of boson star modes of nonzero frequency. We find good agreement between our critical solutions and boson star modes. For critical solutions less than 90% of the maximum boson star mass $M_{\rm max} \simeq 0.633 M_{Pl}^2/m$, a small halo of matter appears in the tail of the solution. This halo appears to be an artifact of the collision between the original boson star and the real field, and does not belong to the true critical solution. It seems that unstable boson stars are unstable to dispersal in addition to black hole formation. Given the similarity in macroscopic stability between boson and neutron stars, we suggest that neutron stars at or beyond the point of instability may also be unstable to explosion.Comment: 26 Pages, 16 Figures, RevTeX. Submitted to Phys. Rev.

Boson stars with negative cosmological constant

“…However, it is a tedious procedure to find the characteristic values of χ 2 for a given value of φ 0 (see [47] for a detailed discussion of this problem in D = 4, Λ = 0 case). For our case, we solved the equations (43), (44) in a neighbourhood of φ c (0), for D = 4 and several negative values of Λ (we consider nodeless unperturbed solutions only).…”

Evolving spherical boson stars on a 3D Cartesian grid

“…evolved for long times (long enough to observe the oscillations of a perturbed star) in spherical symmetry using 1D codes [10,11,12]. The main reason for this is without doubt the difficulty in formulating the evolution equations for the space-time from Einstein's equations when using non-spherical symmetry.…”

“…As I am going to deal only with spherically symmetric Boson Stars, a zero shift is used for stable equilibrium configurations, and a simple but sophisticated driver involving a non-zero shift will prove to be necessary in order to follow the evolution of unstable configurations. The general form of the potential to be studied here is V (|φ|) = 1 2 m 2 |φ| 2 + λ 4 |φ| 4 , which has been the most studied case with 1D codes [10,11,12], among a variety of potentials studied [16,17,18] and others including very general non polynomial potentials [19].…”

“…The main reason for this is without doubt the difficulty in formulating the evolution equations for the space-time from Einstein's equations when using non-spherical symmetry. In spherical symmetry these evolution equations are replaced with the slicing condition and the constraints (see for instance [11,12]). The resulting ODEs can be integrated at each time step during the evolution, which is computationally cheap and allows a constrained evolution under control for very long periods of time.…”

What happens toQballs ifQis so large?

“…As for the boundary conditions of the center and the outer edge, we follow Hayley and Choptuik [20] as follows. For φ, ξ and ̟ at r = 0, we employ a "quadratic fit,"…”