Nonexistence of self-similar solutions containing a black hole in a universe with a stiff fluid or scalar field or quintessence

Abstract

We consider the possible existence of self-similar solutions containing black holes in a Friedmann background with a stiff fluid or a scalar field. We carefully study the relationship between the self-similar equations in these two cases and emphasize the crucial role of the similarity horizon. We show that there is no self-similar black hole solution surrounded by an exact or asymptotically flat Friedmann background containing a massless scalar field. This result also applies for a scalar field with a potential, providing the universe is decelerating. However, if there is a potential and the universe is accelerating (as in the quintessence scenario), the result only applies for an exact Friedmann background. This extends the result previously found in the stiff fluid case and strongly suggests that accretion onto primordial black holes is ineffective even during scalar field domination. It also contradicts recent claims that such black holes can grow appreciably by accreting quintessence. Appreciable growth might be possible with very special matter fields but this requires ad hoc and probably unphysical conditions.

Dark sector impact on gravitational collapse of an electrically charged scalar field

“…Apart from investigations of spacetime structures formed during the collapse in the presence of the dark sector, other tantalizing questions are the mechanism of black hole formation and the behavior of matter accreting onto a nascent black hole taking the cosmological evolution into account. It was claimed that primordial black holes can accrete the surrounding dark energy, phantom energy or ghost condensate very effectively [130,131]. However, the conducted analyses neglected cosmic expansion.…”

Scalar field collapse with negative cosmological constant

“…For a related discussion in the context of an apparent cosmological horizon, see Ref. [37], especially Fig. 6.…”

Analytical solutions of accreting black holes immersed in a ΛCDM model

“…This behaviour may seem outrageous, as the mass diverges in a finite time. However, it has been made clear [11,12,3] that such a result is an artifact of the local test-fluid approximation which does not take into account the backreaction onto the black hole metric, the consequence being the absence of an upper bound for the accretion of a pressureless fluid. Therefore, it cannot be used at all for arbitrarily high dark matter densities and time intervals.…”