Are black holes a serious threat to scalar field dark matter models?

Abstract

Classical scalar fields have been proposed as possible candidates for the dark matter component of the universe. Given the fact that super-massive black holes seem to exist at the center of most galaxies, in order to be a viable candidate for the dark matter halo a scalar field configuration should be stable in the presence of a central black hole, or at least be able to survive for cosmological time-scales. In the present work we consider a scalar field as a test field on a Schwarzschild background, and study under which conditions one can obtain long-lived configurations. We present a detailed study of the Klein-Gordon equation in the Schwarzschild spacetime, both from an analytical and numerical point of view, and show that indeed there exist quasi-stationary solutions that can remain surrounding a black hole for large time-scales.Comment: 34 pages, 13 figure

Scalar field as a Bose-Einstein condensate?

“…Finally, this approach can be extended to more general scenarios, in which the spacetime has rotation, and an analogy could be made with phenomena associated with Bose-Einstein condensates such as vorticity and superfluidity, along the lines of [35]. It is worth noting that these ideas could imply the possibility that a scalar field considered as a Bose-Einstein condensate could account for dark matter halos surrounding galaxies [23][24][25]. Clearly these topics deserve deeper investigation, which will be presented elsewhere [36].…”

“…This case has been already discussed in detail [23,24] within the context of scalar field distributions which remain surrounding a black hole for cosmological times. The metric coefficient in the line element, Eq.…”

“…A detailed discussion has been given in Refs. [23,24], describing how one does indeed have quasi-stationary scalar field distributions which accrete towards the black hole, but at such a slow rate that they can last for cosmological times. We remark that the solutions are quasi-stationary as long as the stationary solutions are forbidden by the black hole no-hair theorems [33].…”

“…There are, however, macroscopic and quantum systems which, under certain circumstances, are described by the same formal equation, with the same mathematical structure. This is the case between a scalar field distribution surrounding a black hole, the so called quasi-bound states [23], and the Bose-Einstein condensate described by the Gross-Pitaevskii equation. We remark that in the former case, it is the space-time curvature, together with the scalar field features, that form an effective potential which contains the scalar field distribution.…”

A Review on the Scalar Field/Bose-Einstein Condensate Dark Matter Model

“…In addition, many numerical simulations have been performed to study the gravitational collapse of the SFDM/BEC model [14,15,28,46,47,48,38,88,89,13]. [24,25] found an approximate analytical expression and numerical solutions of the mass-radius relation of SFDM/BEC halos.…”