  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.
