Noble gravitational atoms: Self-gravitating black hole scalar wigs with angular momentum number
We present new spherically symmetric solutions of the Einstein-Klein-Gordon equations in a quasi-stationary approximation that describe self-gravitating scalar field configurations around a black hole, including angular momentum number $\ell$. An approach analogous to the one which gives rise to $\ell$-boson stars is used here to construct self-gravitating ``gravitational atoms" with $\ell\ge0$. We refer to these new solutions as {\it noble gravitational atoms}, by analogy with noble atoms, which are characterized by closed electron shells. We show that, in the proper limit, noble gravitational atoms approach $\ell$-boson stars globally, displaying noticeable differences only in a region very close to the event horizon. Noble gravitational atoms with $\ell>0$ sometimes present density maxima located at relatively large radii, with small density close to the horizon for $\ell>1$. Furthermore, they do not always present the typical density spike at the event horizon if $\ell > 0$; on the contrary, they sometimes exhibit a small dip there. When $\ell=0$, a spike can appear, but its contribution to the total mass density is always negligible. The size, density, and lifetime of these objects vary significantly depending on the parameters, being in some cases as large as galaxies, as dilute as dark matter, and as long-lived as the Universe itself.