Quasistationary solutions of scalar fields around collapsing self-interacting boson stars

Abstract

There is increasing numerical evidence that scalar fields can form long-lived quasi-bound states around black holes. Recent perturbative and numerical relativity calculations have provided further confirmation in a variety of physical systems, including both static and accreting black holes, and collapsing fermionic stars. In this work we investigate this issue yet again in the context of gravitationally unstable boson stars leading to black hole formation. We build a large sample of spherically symmetric initial models, both stable and unstable, incorporating a self-interaction potential with a quartic term. The three different outcomes of unstable models, namely migration to the stable branch, total dispersion, and collapse to a black hole, are also present for self-interacting boson stars. Our simulations show that for black-hole-forming models, a scalar-field remnant is found outside the black-hole horizon, oscillating at a different frequency than that of the original boson star. This result is in good agreement with recent spherically symmetric simulations of unstable Proca stars collapsing to black holes [1].

Self-interactions can stabilize excited boson stars

“…where µ is the scalar field mass and λ is the parameter controling the quartic self-interactions. This model has been considered, in the context of boson stars, in a number of previous works, including [16][17][18].…”

“…The numerical evaluation of the equations of motion (via a shooting method) is done in units with µ = 1, such that the only input parameter of the model is λ. Also, following [18], we define…”

“…As in previous works [25,26], we solve the Klein-Gordon equation by introducing first-order variables defined as…”

“…We solve the above equations using a numerical-relativity code that assumes spherical symmetry and spherical coordinates, described in [23][24][25][27][28][29]. The BSSN and Klein-Gordon coupled equations are solved using a second-order Partially Implicity Runge-Kutta scheme [30,31].…”

Head-on collisions and orbital mergers of Proca stars

“…Solutions belonging to the latter may have different fates, depending on the initial perturbation and the sign of their binding energy. As their scalar cousins, with and without a self-interacting term [39][40][41][42], unstable solutions with positive binding energy migrate to the stable branch, whereas unstable solutions with a negative binding energy (excess energy) undergo fission; i.e. they disperse entirely.…”