Self-similar cosmological solutions with dark energy. II: black holes, naked singularities and wormholes

Abstract

We use a combination of numerical and analytical methods, exploiting the equations derived in a preceding paper, to classify all spherically symmetric self-similar solutions which are asymptotically Friedmann at large distances and contain a perfect fluid with equation of state $p=(\gamma -1)\mu$ with $0<\gamma <2/3$. The expansion of the Friedmann universe is accelerated in this case. We find a one-parameter family of self-similar solutions representing a black hole embedded in a Friedmann background. This suggests that, in contrast to the positive pressure case, black holes in a universe with dark energy can grow as fast as the Hubble horizon if they are not too large. There are also self-similar solutions which contain a central naked singularity with negative mass and solutions which represent a Friedmann universe connected to either another Friedmann universe or some other cosmological model. The latter are interpreted as self-similar cosmological white hole or wormhole solutions. The throats of these wormholes are defined as two-dimensional spheres with minimal area on a spacelike hypersurface and they are all non-traversable because of the absence of a past null infinity.

12 pages, 19 figures, 1 table, final version to appear in Physical Review D

References in corpus (3)

• Non-existence of self-similar solutions containing a black hole in a universe with a stiff fluid or scalar field or quintessence
• Self-similar cosmological solutions with dark energy. I: formulation and asymptotic analysis
• General Relativistic Self-Similar Solutions in Cosmology

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