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arXiv · 2008.10608

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

C. A. R. Herdeiro·J. Kunz·I. Perapechka·E. Radu·Ya. Shnir
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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, $g_{\mu\nu}$) 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 $\Phi_{(N,\ell,m)}$, which could be realized in the macrocosmos, and those of the linear Schr\"odinger equation in a Coulomb potential, denoted $\Psi_{(N,\ell,m)}$, 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 $m\neq 0$ describe gravitating solitons $[g_{\mu\nu},\Phi_{(N,\ell,m)}]$ without any continuous symmetries. Multipolar boson stars analogue to hybrid orbitals are also constructed.

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C. A. R. Herdeiro, J. Kunz, I. Perapechka, E. Radu, Ya. Shnir. 2020-08-24. Multipolar boson stars: macroscopic Bose-Einstein condensates akin to hydrogen orbitals. https://doi.org/10.1016/j.physletb.2020.136027

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