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

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

2006-04-11

arxiv.org/abs/astro-ph/0604225v3

Phys.Rev.D74:024024,2006

Astronomy and Astrophysics

Astrophysics

17 pages, 6 figures, Accepted for Publication in Phys. Rev. D, Minor Correction

Scientific paper

10.1103/PhysRevD.74.024024

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 {\it ad hoc} and probably unphysical conditions.

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