Abstract
$\ell$-boson stars are static, spherical, multi-field self-gravitating solitons. They are asymptotically flat, finite energy solutions of Einstein's gravity minimally coupled to an odd number of massive, complex scalar fields. A previous study assessed the stability of $\ell$-boson stars under spherical perturbations, finding that there are both stable and unstable branches of solutions, as for single-field boson stars ($\ell=0$). In this work we probe the stability of $\ell$-boson stars against non-spherical perturbations by performing numerical evolutions of the Einstein-Klein-Gordon system, with a 3D code. For the timescales explored, the $\ell$-boson stars belonging to the spherical stable branch do not exhibit measurable growing modes. We find, however, evidence of zero modes; that is, non-spherical perturbations that neither grow nor decay. This suggests the branching off towards a larger family of equilibrium solutions: we conjecture that $\ell$-boson stars are the enhanced isometry point of a larger family of static (and possibly stationary), non-spherical multi-field self-gravitating solitons.
Highlights
Boson stars [1,2] are remarkable gravitational solitons
While perturbing the initial equilibrium configurations adding perturbations that preserve the spherical symmetry, we find that the configuration that was reported to be stable in Ref. [38] remains stable in the timescale we reach in the 3D simulations, run M1000
The results of the previous section indicate that those configurations (M1) that are stable under spherical perturbations do not show nonspherical growing modes
Summary
Boson stars [1,2] (see [3,4] for reviews) are remarkable gravitational solitons. These self-gravitating, localized energy lumps of a complex, massive scalar field have appealing theoretical properties. One must assess if some perturbations deform l-boson stars into acquiring new degrees of freedom In this respect, it was recently proposed that multifield boson stars, in the nonrelativistic regime, could have nonspherical stable configurations [39]. By contrast, spinning Proca stars do not present instabilities under nonaxisymmetric perturbations and they can form dynamically [40] This example shows how the study on nonspherical perturbations unveiled a new relevant dynamical property of boson stars. Zero modes can occur even if there is no instability, as in the Schwarzschild example, indicating, an enlarged family of solutions (Kerr or Reissner-Nordström), of which the initial spacetime (Schwarzschild) is a special case. In this work we use units where G 1⁄4 1 1⁄4 c
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