Olivier Sarbach

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 ℓ. An approach analogous to the one which gives rise to ℓ-boson stars is used here to construct self-gravitating "gravitational atoms" with ℓ ≥ 0. We refer to these new solutions as 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 ℓ-boson stars globally, displaying noticeable differences only in a region very close to the event horizon. Noble gravitational atoms with ℓ > 0 sometimes present density maxima located at relatively large radii, with small density close to the horizon for ℓ > 1. Furthermore, they do not always present the typical density spike at the event horizon if ℓ > 0; on the contrary, they sometimes exhibit a small dip there. When ℓ = 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.

We construct gravitational atoms including self-gravity, obtaining solutions of the Einstein–Klein–Gordon equations for a scalar field (SF) surrounding a non-rotating black hole (BH) in a quasi-stationary approximation. We resolve the region near the horizon as well as the far field one. Our results are relevant in a wide range of masses, from ultralight to MeV SFs and for BHs ranging from primordial to supermassive. For instance, the core of a galactic halo consistent with ultralight dark matter and a BH with a mass comparable to that of Sagittarius A* can be modeled. A density spike near the event horizon, although present, is negligible, contrasting with the prediction in Gondolo and Silk (1999 Phys. Rev. Lett. 83 1719–22) for cold dark matter.

We present a nontrivial extension of the problem of spherical accretion of a collisionless kinetic gas into the standard Schwarzschild black hole. This extension consists of replacing the Schwarzschild black hole by generic static and spherically symmetric black hole spacetimes with the aim of studying the effects of either modified gravitational theories beyond Einstein gravity or matter sources coupled to general relativity on the accretion process. This generalization also allows us to investigate the accretion into other types of black hole spacetimes, such as ones inspired by loop quantum gravity and string theory. To do so, we take into account a large class of static and spherically symmetric black holes whose spacetime is asymptotically flat with a positive total mass, has a regular Killing horizon, and satisfies appropriate monotonicity conditions of the metric functions. We provide the most general solution of the collisionless Boltzmann equation on such spacetimes by expressing the one-particle distribution function in terms of suitable symplectic coordinates on the cotangent bundle, and we calculate the relevant observables, such as particle current density and energy-momentum-stress tensor. Specializing to the case where the gas is described by an isotropic ideal fluid at rest at infinity, we compute the mass accretion rate and compression ratio, and we show that the tangential pressure is larger than the radial one at the horizon, indicating that the behavior of a collisionless gas is different from the one of an isotropic perfect fluid. Our general relations for the spacetime observables are given in terms of the generic metric functions which are determined by the parameters that characterize the black hole. As a concrete example, we apply our generic formulae to two special black hole spacetimes, namely the Reissner–Nordström black hole and a loop quantum corrected black hole. We explore the effects of the free parameters on the observables and accretion rate, and we compare the results with those corresponding to the standard Schwarzschild black hole.

The conditions for the existence of the Chapman–Enskog first-order solution to the Boltzmann equation for a dilute gas are examined from two points of view. The traditional procedure is contrasted with a somehow more formal approach based on the properties of the linearized collision operator. It is shown that both methods lead to the same integral equation in the non-relativistic scenario. Meanwhile, for relativistic systems, the source term in the integral equation adopts two different forms. However, as we explain, this does not lead to an inconsistency. In fact, the constitutive equations that are obtained from both methods are shown to be equivalent within relativistic first-order theories. The importance of stating invariant definitions for the transport coefficients in this context is emphasized.