Transitioning from Finite to Infinite Mass in a Black Hole

[Cody Richeson]

So, according to physicsoftheuniverse.com, "In the centre of a black hole is a gravitational singularity, a one-dimensional point which contains infinite mass in an infinitely small space, where gravity become (sic) infinite and space-time curves infinitely, and where the laws of physics as we know them cease to operate."

Now, if my understanding is correct (and I doubt it is), the previous state of the black hole was that of a star of a mass which has the potential to yield a black hole once that star has died. Obviously, while the star is alive, its mass is finite, its gravitational pull is finite and the manner in which it curves space-time is finite. What exactly happens that causes these variables to become infinite? I can picture them becoming arbitrarily large, but infinity is not about growing or shrinking drastically in size; it's not about any particular numerical value at all.

Furthermore, I find it confusing that we know it is infinite, because what indicates this? If you measure something, shouldn't the result be a finite value? How could you possibly measure something and conclude that it is infinite in a particular regard?

 

[DaveC426913]

So, according to physicsoftheuniverse.com, "In the centre of a black hole is ... a one-dimensional point which contains infinite mass in an infinitely small space, where gravity become (sic) infinite and space-time curves infinitely,

All false.

and where the laws of physics as we know them cease to operate."

True. No infinities, just no laws.

Now, if my understanding is correct (and I doubt it is),

It is correct.

the previous state of the black hole was that of a star of a mass which has the potential to yield a black hole once that star has died. Obviously, while the star is alive, its mass is finite, its gravitational pull is finite and the manner in which it curves space-time is finite.

Correct.

What exactly happens that causes these variables to become infinite?

Badly written websites.

 

[Cody Richeson]

Well, that brings up three additional questions:
1) Why are there claims of these values being infinite if it's patently wrong?
2) If it's not infinite, does it just mean these values are very extreme?
3) Is the center of a black hole really a one-dimensional point, and if so, how is it possible for the topology of an area of spacetime able to condense into a point which has no radius?

 

[Vanadium 50]

Why are there claims of these values being infinite if it's patently wrong?

What? Something is wrong on the internet? How could that happen?

 

[Nugatory]

So, according to physicsoftheuniverse.com

A good site to avoid, or at least to approach with caution...

Now, if my understanding is correct (and I doubt it is)

Your understanding here is correct and they're wrong.

Furthermore, I find it confusing that we know it is infinite, because what indicates this? If you measure something, shouldn't the result be a finite value? How could you possibly measure something and conclude that it is infinite in a particular regard?

There are a bunch of threads (some over in the astrophysics section) about what happens at the center of a black hole that you may find helpful. A quick summary: We expect that the mass at the center of a black hole does not really compress down to a point of zero volume, infinite density, and infinite gravity. General relativity says that would happen if nothing prevents it... but that is best interpreted as a powerful argument that something will happen to prevent it, and we just don't know what yet.

There's an analogy from classical physics: You're likely familiar with Coulomb's law for the electrical force, $F=CQ_1Q_2/r^2$, that says that the electrical force between two charged particles is inversely proportional to the square of the distance between them... notice that this law predicts that if I put two charged particles on top of one another so $r=0$, the force is infinite. But we don't really expect that to happen; instead we take it as a hint from mother nature that Coulomb's law probably doesn't work when the particles are very near one another. And indeed that's the case; when the distance scale is very small to we have to use quantum mechanics, and it predicts different results at that scale.

 

[Cody Richeson]

I'll be honest, I've heard Coulomb's law described many times and I don't really understand it. When I see terms like "inversely proportional" and "square of the distance between them," I am unable to translate the abstraction of that idea into something I can visualize.

 

[Nugatory]

I'll be honest, I've heard Coulomb's law described many times and I don't really understand it. When I see terms like "inversely proportional" and "square of the distance between them," I am unable to translate the abstraction of that idea into something I can visualize.

That's because math works better than words if you want to understand physics. But here it's OK. You can just plug $r=0$ into the equation, watch an infinity pop out, and you don't need to do any visualizing to know that no matter how good the equation is under most conditions, it can't be an accurate description of the physics when $r=0$.

The infinity that appears when you plug "distance from the center of the black hole is zero" into the equations of general relativity is similar - the correct conclusion is not that there is infinite gravity at a distance of zero from the center (in other words, right at the center), it is that the equations of GR cannot be accurately describing all the physics there.

Your intuition that it can't really be infinite is good.