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

C. A. R. Herdeiro; J. Kunz; I. Perapechka; E. Radu; Ya. Shnir

doi:10.1016/j.physletb.2020.136027

paper

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

arXiv:2008.10608 · doi:10.1016/j.physletb.2020.136027

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, $g_{μν}$ ) boson stars, composed of a single complex scalar field, $Φ$ , 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 $Φ_{(N, ℓ, m)}$ , which could be realized in the macrocosmos, and those of the linear Schrödinger equation in a Coulomb potential, denoted $Ψ_{(N, ℓ, m)}$ , that describe the microcosmos. In both cases, the solutions are classified by a triplet of quantum numbers $(N, ℓ, m)$ . 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 $[g_{μν}, Φ_{(N, ℓ, m)}]$ without any continuous symmetries. Multipolar boson stars analogue to hybrid orbitals are also constructed.

arXiv comment5 pages, 4 figures

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

Abstract

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