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Can a primordial black hole or wormhole grow as fast as the universe? (English) Zbl 1200.83001
Summary: This review addresses the issue of whether there are physically realistic self-similar solutions in which a primordial black hole is attached to an exact or asymptotically Friedmann model for an equation of state of the form $p=\left(\gamma -1\right)\rho {c}^{2}$. In the positive-pressure case $\left(1<\gamma <2\right)$, there is no solution in which the black hole is attached to an exact Friedmann background via a sonic point. However, there is a one-parameter family of black hole solutions which are everywhere supersonic and asymptotically quasi-Friedmann, in the sense that they contain a solid angle deficit at large distances. Such solutions exist providing the ratio of the black hole size to the cosmological horizon size is above some critical value and they include ‘universal’ black holes with an apparent horizon but no event horizon. In the stiff case ($\gamma =2$), there is no self-similar solution in an exact background unless the matter turns into null dust before entering the event horizon; otherwise the only black hole solutions are probably asymptotically quasi-Friedmann universal ones. For a dark-energy-dominated universe ($0<\gamma <2/3$), there is a one-parameter family of black hole solutions which are properly asymptotically Friedmann (i.e. with no angle deficit) and the ratio of the black hole size to the cosmological horizon size is below some critical value. Above this value, one finds a self-similar cosmological wormhole solution which connects two asymptotic regions: one exactly Friedmann and the other asymptotically quasi-Friedmann. We also consider the possibility of self-similar black hole solutions in a universe dominated by a scalar field. This is like the stiff fluid case if the field is massless, but the situation is less clear if the scalar field is rolling down a potential and therefore massive, as in the quintessence scenario. Although no explicit asymptotically Friedmann black hole solutions of this kind are known, they may exist if the black hole is not too large.
##### MSC:
 83-02 Research monographs (relativity) 85-02 Research monographs (astronomy and astrophysics) 85A40 Cosmology (astronomy and astrophysics) 83F05 Relativistic cosmology 83C57 Black holes 83C15 Closed form solutions of equations in general relativity 83C55 Macroscopic interaction of the gravitational field with matter (general relativity)