Theoretically, if a black hole grew to a huge scale such that the effect of dark energy was large, could the black hole become 'normal' space again (i.e. no horizon or singularity)? What I'm trying to understand is, does dark energy 'uncurve' space-time?

  • $\begingroup$ No one knows what the dark energy is, so I would think that no definite answer for your question exists. Besides, strictly speaking, there is no singularity on black hole horizon. $\endgroup$ – user23660 Oct 29 '13 at 5:27
  • $\begingroup$ I meant to write singularity or horizon. What I'm trying to figure out is whether the expansion would reduce the curvature of the black hole, or just 'stretch' it $\endgroup$ – Chris L. Oct 29 '13 at 13:02

The situation you are describing is very similar to (but not exactly like) a Schwarzschild-de Sitter universe. That is a spacetime that is flat, infinite in size, expanding with a cosmological constant, and contains a massive body (such as a black hole). The metric for such a spacetime is: $$ds^2=-\left(1-\frac{2GM}{r}-\frac{\Lambda}{3}r^2\right)dt^2+\left(1-\frac{2GM}{r}-\frac{\Lambda}{3}r^2\right)^{-1}dr^2+r^2d\Omega_2^2$$ where $\Lambda$ is the cosmological constant and $M$ is the mass of the black hole. This is different from our universe because it does not contain a time-dependent scale factor on the spatial terms. However, that would only accelerate what I am about to describe. For spacetimes such as this, an event horizon is said to exist at the point where the terms in front of $dt^2$ and $dr^2$ vanish.

For a small black hole, $GM\ll\frac{1}{\sqrt\Lambda}$, you can see there would be event horizons at $r=2GM$ and at $r=\sqrt{\frac{3}{\Lambda}}$. The horizon at $2GM$ is the black hole horizon and the other horizon is due to the expansion of space exceeding the speed of light. However, and this is the part that will interest you, as the size of the black hole grows, the two horizons get closer to one another. We can see that for large values of $GM$ there are no real solutions, so no horizons form. Restating: A sufficiently massive black hole in an expanding universe could not form an event horizon. However, the singularity would still exist and spacetime would be heavily curved.

Now, since our universe has a time-dependent scale factor, and since we experience accelerated expansion (something that is inevitable in a model of a flat universe with dark energy as a constant energy density), this effect would effectively lower the required mass to prevent a black hole from having an event horizon. Having said all this, there is no black hole in the observable universe that could fall under this effect. In order for the expansion of space to remove the event horizon, the black hole would have to be on the order of the size of the visible universe. Not a particularly liveable situation.


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