When a new black hole forms does the universe shrink/contract?

Question

I know that scientists debate if the universe is infinite, but for the purposes of this question let’s assume that the universe is finite and has a boundary. When a new black hole forms does the diameter of the universe contract slightly, since part of the space-time that makes up the universe gets folded up into the black hole?

Answer 1

Imagine that a spherically symmetric, uncharged, and non-rotating star collapses to a black hole. According to the Birkhoff theorem, the metric outside the star does not change. Also, no gravitational radiation is emitted during this collapse. Thus, from the standpoint of spacetime geometry, the universe is unaffected when stars collapse to black holes.

For example, hypothetically, if our Sun were magically replaced by a black hole of the same mass, the orbit of the Earth and all other planets would not change. At a sufficient distance, the spacetime around a black hole is the same as around a star of the same mass (assuming no charge or rotation).

Therefore, in the sense of your question, black holes do not “fold” spacetime.

Answer 2

The answer is "no". Cosmology - the field that studies the universe on the largest scales - is what we must look at, because we are assuming that the universe is finite and has a boundary. Modern cosmology is built on the Friedmann–Lemaître–Robertson–Walker metric (FLRW metric), which you can read about here. It looks like this:

$$ds^2 = dt^2 - a(t)^2\left(\frac{dr^2}{1-kr^2} + r^2d\theta^2+r^2\sin^2(\theta)d\phi^2\right)$$

If we assume the universe is finite and has a boundary, then we are assuming the universe is closed, and $k=1$. Here $r$, $\theta$ and $\phi$ are the standard spherical polar coordinates, $t$ is time, and $a$ is the so-called scale factor that is a measure of the size of the universe.

Note this equation does not contain the number of black holes in the universe. So the answer to your question is "no".

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Another way to think about this (and might be closer to what you're thinking of) is that when you are dealing with infinities, our intuition breaks down. Even if we assume the universe is finite and has a boundary, there are still infinities. For example, the number of real numbers between $0$ and $1$ is the same as the number of real numbers between $0$ and $2$. This means that, in principle, we can compress the x-axis of the whole universe into a line between $0$ and $1$, and not lose any information. Something similar happens near a black hole. The axis distorts (corresponding to "folding" of spacetime) but you still don't need more space to compensate.