### Are black holes expanding?

• We know that it is a commonly heard claim that in every black hole there is a universe. It is also believed that the universe is expanding. If we use both of these, can we conclude that every black hole is expanding?

*We know that it is famous theory that in every black hole there is a universe .* - I don't think that any mainstream theory states this.

"Baby Universes" is a rather speculative idea, but it is based on sound principles.

We don't even know if they exist.

• Most$^\dagger$ black holes are indeed expanding, but not because the Universe is expanding. Rather, their size (more precisely their Schwarzschild radius) increases proportionally to their mass, so they grow as they accrete more matter.

It is a common misconception that everything expands along with the expanding Universe. It doesn't. On small scales, i.e. black holes, planets, stars, galaxies, and even galaxy groups, gravity ensures that these things don't increase in size. Only on large scales, i.e. galaxy clusters and beyond, does the expanding Universe pull everything apart.

As for the theory about a universe inside, I… I don't even wanna go there. I'll just refer to HDE 226868's comment.

$^\dagger$Very small black holes will decrease in size due to Hawking evaporation.

think we have to at least accept that a cosmological constant could cause the expansion of event horizons (see John Rennie's answer).

@JohnDavis: Yes okay, you're right that the effect is non-zero, but it's completely negligible for our Universe.

@pela Are you saying large black holes are not shrinking due to Hawking radiation?

@ThisPlayName: No sorry, that's not what I meant. BHS _are_ shrinking due to Hawking radiation, but most regular-sized BHs accrete matter — and hence grow — at a faster rate than they radiate. Hawking radiation flux is inversely proportional to the size, so very small BHs (sub-stellar size) can shrink faster than the matter they accrete makes them grow, and may thus be able to evaporate completely.

• In the standard ΛCDM cosmology, the expansion of the universe is modelled by a cosmological constant $\Lambda$, usually interpreted as a constant density of dark energy.

A nonzero cosmological constant somewhat modifies the usual black hole geometries. For example, the simplest Schwarzschild black hole (isolated, uncharged, nonrotating) is described by
$$\mathrm{d}s^2 = -\left(1-\frac{2GM}{r}\right)\mathrm{d}t^2 + \left(1-\frac{2GM}{r}\right)^{-1}\mathrm{d}r^2 + r^2\mathrm{d}\Omega^2\text{,}$$
which with a nonzero $\Lambda$ would be the Schwarzschild-de Sitter spacetime described by the replacement
$$\left(1-\frac{2GM}{r}\right)\mapsto\left(1-\frac{2GM}{r}-\frac{\Lambda r^2}{3}\right)\text{.}$$

Therefore, a cosmological constant would not cause a black hole to expand or contract. Rather, its size (i.e. of the horizon) is slightly modified by the cosmological constant. The same kind of thing happens to other bound systems, such as star systems and galaxies: in principle the expansion of the universe modifies their size by a slight amount, but the forces that bind them simply find an equilibrium against cosmic expansion.

It would take some extended model of dark energy, in which it is not a constant, to expand of shrink black holes. But there is currently no evidence of such a thing.

Side note: since the Hawking temperature of any astrophysical black hole would be much lower than the surrounding space (e.g., cosmic microwave background), we can expect black holes to slightly expand due to absorbing more energy from their environment than their lose by Hawking radiation. But this effect is both tiny and has a completely different mechanism than the expansion of the universe.

Large black holes are usually expanding by an incredibly small amount as they suck in more stuff (gases, planets, stars, etc.) through gravity. So they are expanding but not because of our expanding universe.

Exceptions

According to Wikipedia, small black holes might shrink. Stephen Hawking predicts that all black holes have radiation. Small black holes, that suck in less, might emit more energy than they pull in, so they theoretically shrink and close.

Big Asterisk

There are many additional details that could be included in this thread. I think the most important to point out is that fifty years ago black holes were still largely science fiction. So it's a relatively new science. And even if we had been studying them for 200-300 years, they're hard to observe and practically impossible to experiment with. Point being, most black hole knowledge is actually black hole theory.

Observing Black Holes

Here's a relevant Wiki excerpt:

In June 2008, NASA launched the Fermi space telescope, which is
searching for the terminal gamma-ray flashes expected from evaporating
primordial black holes. In the event that speculative large extra
dimension theories are correct, CERN's Large Hadron Collider may be
able to create micro black holes and observe their
evaporation.

Relevant Detail on Black Holes

Black holes were once massive stars. Stars have massive gravity but they don't collapse until they run out of fuel. When they do run out of fuel, they expand then collapse. Big stars have so much gravity that they collapse into a small sphere with gravity so intense that light can't escape it. That is when a black "hole" is born. Really, it's more like a black sphere. It appears to be a hole only because no light escapes. Inside the sphere there could be a hole, but no one knows.

Further Explanation on Black Hole Expansion

Bigger stars have more mass so when they collapse, they have more gravity and the perceived "hole" is bigger. Typically, large galaxies have large black holes at their center and small galaxies have small black holes. Over time, the black hole will pull more matter (gases, planets, asteroids, etc.) into its sphere of blackness. This adds to its mass and slowly increases its gravity. More gravity means a wider radius of black where from which not even light escapes.

When does a black hole stop growing and why? That's hard to answer because we have no data about the inside of a black hole. Some people theorize the immense gravity bends space/time to create a wormhole. Many questions about space are being answered in our lifetime by observing and experimenting. Black holes are hard to observe and even harder to experiment with. Most "answers" in our lifetime will be more theory than proven physics.

Just a couple comments (nitpicks, really). I feel like you unjustly cast the theories behind black holes in a poor light. The Schwarzschild solution is almost 100 years old - so there's some solid theory behind it - and in the 40 or so years since Cygnus X-1 was discovered, we've learned a lot. So I'm not sure your characterization of the black hole science as "young" is, while accurate, a tad misleading. Additionally, I feel like you lean a bit to the "just a theory" side of things. Experiment is better than theory, but a theoretical proof can create an established cornerstone of science.

[Continued; I was out of characters!] That said, I don't want to sound too harsh. The other 95% of this answer is excellent, so +1 and welcome to Astronomy Stack Exchange!

Thanks. I can nit-pick myself so no offense taken and thanks for the welcome. I intended to write it in that tone as I can't provide a good answer. Unlike planets and stars, black hole life-cycles are still mysterious to us. We understand their catalyst but nothing beyond that. We don't know if the matter sucked in is being ejected somewhere else in our universe or another dimension or just added to a dense core. We don't know about their deaths. If they close, what happened to that dense core with the immense gravity? Black holes are more perplexing than dark matter, neutrinos, etc.

That's a fair point, and one I perhaps hadn't considered enough.