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

TL;DR

This paper classifies self-similar solutions in dark energy-dominated universes, revealing black holes that can grow rapidly, naked singularities, and non-traversable wormholes within a unified analytical and numerical framework.

Contribution

It provides a comprehensive classification of spherically symmetric self-similar solutions with dark energy, including black holes, naked singularities, and wormholes, extending previous work to accelerated expansion scenarios.

Findings

Black holes can grow as fast as the Hubble horizon in dark energy universes.

Existence of naked singularities with negative mass.

Identification of non-traversable wormhole solutions.

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.