$\ell$-boson stars are static, spherical, multifield 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 nonspherical 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, nonspherical perturbations that neither grow nor decay. This suggests the branching off toward 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), nonspherical multifield self-gravitating solitons.

• Received 24 April 2020
• Accepted 19 May 2020

DOI:https://doi.org/10.1103/PhysRevD.101.124020