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The expansion of the Friedmann universe is accelerated in this case. We find a one-parameter family of self-similar solutions dting direct 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. These wormholes are generally traversable, where we define a wormhole naked as koga two-dimensional sphere with minimal area on a spacelike hypersurface.
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