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arXiv · 2605.27529

Existence of nonrelativistic $\ell$- and multi-$\ell$-boson stars and their radial stability

Emmanuel Chávez Nambo·Olivier Sarbach
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Abstract

Using direct methods of the calculus of variations we establish the existence of an infinite class of spherically-symmetric solutions to the multi-field Schr\"odinger-Poisson system. This is achieved by proving that the energy functional admits a global minimum when restricted to the set of vector-valued wave functions in the Sobolev space $H^1$ which are invariant with respect to a suitable representation of the rotation group and whose components have fixed $L^2$-norms. Additionally, we show that these minima correspond to solutions which are orbital stable with respect to perturbations of the wave function within this set. The generalization to include an external potential and some important properties of the minima are also discussed.

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Emmanuel Chávez Nambo, Olivier Sarbach. 2026-05-26. Existence of nonrelativistic $\ell$- and multi-$\ell$-boson stars and their radial stability. https://arxiv.org/abs/2605.27529

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