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

Authors:
  • THTomohiro Harada
    Tomohiro Harada
  • HMHideki Maeda
    Hideki Maeda
  • BCB. J. Carr
    B. J. Carr
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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 applies even if there is a scalar potential, as in the quintessence scenario. 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.