How can black holes with varying masses have the same extreme characteristics?

[Soul Intent]

TL;DR Summary

I'm not suggesting there aren't simple answers to the questions I'm about to pose. It's possible I'm missing something obvious, I'd appreciate feedback. Thanks!

Shouldn't all black holes have the same density? Since all are assumed to contain a singularity (infinite density). Also, depicting spatial curvature due to gravity in terms of a two-dimensional fabric is very misleading. Whether you're imaging a black hole, or a star. We live in a three-dimensional reality, so gravitational curvature should be represented in that way.
Lastly, based on my individual understanding, all black holes can trap light. It's a characteristic which defines them, apart from everything else in the universe. Their mass creates a region which, if crossed, nothing can escape. However, lately I've been reading up on some questions I've had for a while. It seems as though black holes vary in mass, from very small (say 15 solar masses) to very large (billions of solar masses). As a general rule of thumb, stars at least 10 times the mass of our sun die in supernovae which in effect creates a black hole. Now, my question is should not all black holes be, from their very nature, exponentially larger in mass than even the heaviest star in the universe? Take cygnus X1 for example. In order to prove it was a black hole, it had to be no less than at least 3 solar masses. This confuses me. Stating this, suggests that cygnus weighs less than some stars. It's final mass was discovered to be 15 solar masses, but my confusion still stands. There are some stars that outweigh ours by 10 or even 20 times. Yet, this particular black hole is only 15 solar masses? So, how much mass does it take to ultimately trap light forever? Or slow time to a stand still?

My theory is that every black hole in the universe must be more massive than anything else that can possibly exist, since nothing else can slow time or trap light in such an extreme fashion. So in the case of cygnus X1, 15 solar masses should easily be determined to be significantly less massive than any black hole. Yet, it's regularly regarded as the first black hole to be discovered. They originally detected cygnus by it's companion stars orbit, and from the high energy X-ray radiation coming from a seemingly invisible source. So it must be a black hole, right? Although, it only weighs in at 15 times the mass of our sun. The X-rays were coming from it's accretion disk spinning at half light speed, and heated to 10s of millions of degrees. If you ask me, such a disk would be very bright and would be easily seen. But apparently the disk wasn't recognized until cygnuss' mass was determined which unquestionably made it a black hole- of 15 solar masses.
I understand supermassive black holes. Something being millions or billions times heavier than our sun, one can imagine strange things would occur. Like light being unable to escape, or time slowing to the point where if someone were to watch something fall in, it would never appear to cross the event horizon. Basically, how can a black hole that weighs less than some stars slow time drastically, and trap light? If this is possible, there would be many objects in the cosmos capable of slowing time and trapping light; which would undoubtedly change the nature of the universe itself.

Thoughts.

 

[Ibix]

Shouldn't all black holes have the same density?

Black holes don't have a well-defined interior volume, so they don't have a density. Sometimes people quote their mass divided by the cube of the Schwarzschild radius (defensible in some senses, but not really a density), which implies a "density" that decreases with size.

Since all are assumed to contain a singularity (infinite density).

This is not an accurate description of a black hole singularity, although you will see it in pop science sources.

depicting spatial curvature due to gravity in terms of a two-dimensional fabric is very misleading.

True. You will not see that except in pop science sources.

Now, my question is should not all black holes be, from their very nature, exponentially larger in mass than even the heaviest star in the universe?

No. Their mass cannot exceed the star they formed from, plus any mass they subsequently swallow (there are a few caveats to that, but that's basically it). Where would extra mass come from?

So, how much mass does it take to ultimately trap light forever?

Any mass will do, as long as it is contained within its Schwarzschild radius. You could have a black hole with the mass of the Earth. The ten solar mass limit is just because there's no way for a smaller star to collapse into a black hole - its matter can resist the collapse. That doesn't mean that smaller black holes are impossible in principle - just that we know of no way for them to form.

Or slow time to a stand still?

This is another inaccurate, but very common in pop sci, description of a black hole's event horizon.

My theory

...appears to be based on a lot of misunderstandings from reading wildly inaccurate descriptions of black holes. You may also wish to review Physics Forums rules on personal theories - the short form is "we don't allow them here".

 

[Orodruin]

Summary: I'm not suggesting there aren't simple answers to the questions I'm about to pose. It's possible I'm missing something obvious, I'd appreciate feedback. Thanks!

Shouldn't all black holes have the same density?

Black holes do not have a density. The Schwarzschild solution is a vacuum solution.

Summary: I'm not suggesting there aren't simple answers to the questions I'm about to pose. It's possible I'm missing something obvious, I'd appreciate feedback. Thanks!

Since all are assumed to contain a singularity (infinite density).

This is incorrect. The singularity of the Schwarzschild solution is more similar to a moment in time than a place in space. As such, it does not make sense to talk about a density for the singularity.

Summary: I'm not suggesting there aren't simple answers to the questions I'm about to pose. It's possible I'm missing something obvious, I'd appreciate feedback. Thanks!

Also, depicting spatial curvature due to gravity in terms of a two-dimensional fabric is very misleading. Whether you're imaging a black hole, or a star. We live in a three-dimensional reality, so gravitational curvature should be represented in that way.

No it should not. It is not spatial curvature, it is spacetime curvature. Spatial curvature is not sufficient, you need to consider four dimensions, not three, to describe gravitation in our universe. Any two-dimensional image is just popular science, nobody actually uses this to do computations.

Summary: I'm not suggesting there aren't simple answers to the questions I'm about to pose. It's possible I'm missing something obvious, I'd appreciate feedback. Thanks!

So, how much mass does it take to ultimately trap light forever?

It depends on how tight you can pack that mass, which in turn depends on what mechanisms are available to counteract gravitational attraction. A black hole can a priori have any mass, it is just a question of how they väcan be created.

Summary: I'm not suggesting there aren't simple answers to the questions I'm about to pose. It's possible I'm missing something obvious, I'd appreciate feedback. Thanks!

My theory is that every black hole in the universe must be more massive than anything else that can possibly exist

This is personal speculation (and also quite wrong), which is not allowed on PF.

 

[PeterDonis]

My theory is

As @Orodruin has already pointed out, personal theories are not allowed on PF. Please take note.

how can a black hole that weighs less than some stars slow time drastically, and trap light?

Because black holes are much more compact than ordinary stars, or even than white dwarfs or neutron stars. It's their compactness that leads to light not being able to escape them, not their mass.

 

[PeterDonis]

If you ask me, such a disk would be very bright and would be easily seen.

It was easily seen--in X-rays. It is not easily seen in visible light because it's not emitting much visible light; it's emitting mostly X-rays.

 

[PeterDonis]

We live in a three-dimensional reality

No, we live in a four-dimensional reality, and the curvature produced by massive objects is four-dimensional spacetime curvature, as @Orodruin has already mentioned.

 

[Soul Intent]

I'm not trying to defend one or come up with a theory, I was just saying that was my interpretation of it. So honestly I don't really care what's allowed or not allowed on here, I'm entitled to whatever I want to say and how I want to say it. I also don't understand why you're insistant on being rude and condescending toward me, because I am looking for feedback. I've never been in any forums before so lighten up. I'm not sure if the responses were multiple people or just one, but either way there's no need to act like you're some forum god that calls the shots and demeans people because they don't see it the same way you do. I'm aware of most of the things you said, but you're also saying things that are speculative. So just chill out and have a conversation like a normal human, stop acting all high and mighty. If I'm wrong, explain why. Don't act offended because I don't understand something the way you do. Also this "pop sci" you keep saying, like I'm not exactly sure what that means, but i get my information from books, not stupid shows on the science channel. It's that's what you're referring to. So I apologize if I broke some rule or something, but what is PF policy on being ignorant and demeaning?

 

[Soul Intent]

As @Orodruin has already pointed out, personal theories are not allowed on PF. Please take note.
Because black holes are much more compact than ordinary stars, or even than white dwarfs or neutron stars. It's their compactness that leads to light not being able to escape them, not their mass.

Density. Got it. Thank you.

 

[PeterDonis]

Density.

No, not density. Compactness. As has already been pointed out, a black hole does not have a well-defined volume, so it does not have a well-defined density. But it does have a well-defined surface area, the area of the horizon; and this surface area is much smaller than the surface area of an ordinary star with the same mass, or a white dwarf of the same mass, and is significantly smaller even than the surface area of a neutron star with the same mass. The smallness of the surface area for a given mass is what "compactness" refers to for a black hole.

 

[PeterDonis]

I'm not trying to defend one or come up with a theory

Then saying "My theory is..." was not a good choice of words. "My interpretation..." would have been better.

honestly I don't really care what's allowed or not allowed on here, I'm entitled to whatever I want to say

Yes, and as a moderator, I'm entitled to enforce the rules of the forum. And the attitude displayed in this post of yours has just earned you a warning.

I also don't understand why you're insistant on being rude and condescending toward me

Drawing attention to the forum rules is not "rude and condescending". It's a normal part of how forums work.

I've never been in any forums before

Then you might want to consider the possibility that you are unfamiliar with how forums work and should not immediately assume that people are being rude and condescending when they are simply trying to communicate to a newcomer what the forum rules and norms are.

I'm aware of most of the things you said, but you're also saying things that are speculative.

Nothing I or @Orodruin or @Ibix said was speculative. The standard GR model of black holes is extremely well understood after decades of theoretical and observational work.

this "pop sci" you keep saying, like I'm not exactly sure what that means, but i get my information from books

Books that are not textbooks are also pop science.

 

[Ibix]

I shan't reiterate Peter's post. I will just observe that I did provide several corrections, I didn't just say "you're wrong".

Also this "pop sci" you keep saying, like I'm not exactly sure what that means, but i get my information from books, not stupid shows on the science channel. It's that's what you're referring to.

Unfortunately, on the topic of relativity, any source that doesn't have a lot of maths is (at best) vaguely descriptive. It's very likely to be outright wrong, because attempting to phrase this stuff in natural language inevitably means compromising accuracy, and what the author intends to say isn't necessarily what you read.

A rule of thumb: if you don't find an average of more than one formula per page, it's pop sci. Great for enthusiasm, poor for understanding. That applies slightly less in a discussion forum like this one because some back-and-forth is possible to iron out misunderstandings. But, fundamentally, in physics if you don't know the maths you don't know the topic.