Multipolar boson stars: macroscopic Bose-Einstein condensates akin to hydrogen orbitals

DOI10.1016/J.PHYSLETB.2020.136027zbMATH Open1476.85003arXiv2008.10608OpenAlexW3080963028MaRDI QIDQ2231475

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Publication date: 29 September 2021

Published in: (Search for Journal in Brave)

Abstract: Boson stars are often described as macroscopic Bose-Einstein condensates. By accommodating large numbers of bosons in the same quantum state, they materialize macroscopically the intangible probability density cloud of a single particle in the quantum world. We take this interpretation of boson stars one step further. We show, by explicitly constructing the fully non-linear solutions, that static (in terms of their spacetime metric, $g_{muu}$) boson stars, composed of a single complex scalar field, $Phi$, can have a non-trivial multipolar structure, yielding the same morphologies for their energy density as those that elementary hydrogen atomic orbitals have for their probability density. This provides a close analogy between the elementary solutions of the non-linear Einstein--Klein-Gordon theory, denoted $Ph{i}_{(N,ell,m)}$, which could be realized in the macrocosmos, and those of the linear Schr"odinger equation in a Coulomb potential, denoted $Ps{i}_{(N,ell,m)}$, that describe the microcosmos. In both cases, the solutions are classified by a triplet of quantum numbers $(N,ell,m)$. In the gravitational theory, multipolar boson stars can be interpreted as individual bosonic lumps in equilibrium; remarkably, the (generic) solutions with $meq0$ describe gravitating solitons $[g_{muu},Ph{i}_{(N,ell,m)}]$ without any continuous symmetries. Multipolar boson stars analogue to hybrid orbitals are also constructed.

Full work available at URL: https://arxiv.org/abs/2008.10608

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