What Determines the Size and Density of a Black Hole?

[Physics101]

Hi all,

Here are few Black Hole related question. I’m more of a visual person and it’s been a while since my college Physics/Calculus days, so please excuse the lack of fundamentals.

Given what we know about Black Holes, is there a widely accepted visualization of what it might look like? For example, is it fair to say that Black Hole “lacks” empty space? In other words, is it a region of space-time that is completely occupied by matter without any vacuum in between? If so, what form of matter is it composed of (quarks?).

If the above were true, at what speed would sound (vibration) travel within the Black Hole? Would it still respect the speed limit of “c” or does this break down in a singularity?

Are all Black Holes equally dense? By this I mean, is there a linear relationship between the size and the mass of Black Holes? Also, is this in any way confined to Plank’s constant?

Finally, is there such thing as a quantum Black Hole? For instance, can the smallest known particle (or the matter that Black Holes are composed of) be considered a miniature Black Hole or are there restrictions in definition of something being called a Black Hole (such as size or minimum mass, etc.)?

Thanks in advance for your replies.

 

[JesseM]

Given what we know about Black Holes, is there a widely accepted visualization of what it might look like? For example, is it fair to say that Black Hole “lacks” empty space? In other words, is it a region of space-time that is completely occupied by matter without any vacuum in between?

No, the opposite actually. According to general relativity, in a black hole gravity has overwhelmed all other forces that could keep the bits of matter it's composed of apart from each other, so all the matter has collapsed into a single point of zero volume and infinite density, the "singularity". When people talk about the size of a black hole, they're talking about the "event horizon", which marks the distance from the singularity beyond which it is impossible for even light to escape being inevitably pulled in toward the singularity. So, the spacetime inside the event horizon but outside the singularity should be empty, aside from stuff that's in the process of falling into the singularity.

Most physicists think the singularity represents a place where general relativity breaks down, and that a theory of quantum gravity would remove the infinities associated with the singularity--perhaps instead of being crushed to infinite density, the matter in a black hole would just be crushed to the Planck density where quantum gravitational effects are thought to become significant, and who knows what would happen at that point.

Finally, is there such thing as a quantum Black Hole? For instance, can the smallest known particle (or the matter that Black Holes are composed of) be considered a miniature Black Hole or are there restrictions in definition of something being called a Black Hole (such as size or minimum mass, etc.)?

This is again an issue of quantum gravity, in general relativity there would be no minimum mass, but it's thought that quantum gravity would imply that the Planck mass is the smallest possible for a black hole. This is around 10^-5 grams, about the mass of a flea--much larger than any known elementary particle.

 

[Physics101]

No, the opposite actually. According to general relativity, in a black hole gravity has overwhelmed all other forces that could keep the bits of matter it's composed of apart from each other, so all the matter has collapsed into a single point of zero volume and infinite density, the "singularity". When people talk about the size of a black hole, they're talking about the "event horizon", which marks the distance from the singularity beyond which it is impossible for even light to escape being inevitably pulled in toward the singularity. So, the spacetime inside the event horizon but outside the singularity should be empty, aside from stuff that's in the process of falling into the singularity.

Interesting. I did further research and reading into the concept of "Singularity" and found your description to be accurate. I suppose that this infinite density concept is relative to the outsider's frame of reference, so is it possible that within the Event Horizon, everything is proceeding as usual -- infiinitely collapsing towards the singularity? If so, is this not a reversed picture of our Universe expanding into infinity? Also, since the enormous gravitational curvature caused by the Black Hole can also be considered infinite, shouldn't the region inside the Event Horizon also be considered infinite as far as Space-Time goes? Assuming that's true, can Black Hole be considered a form of a sub-Universe?

Most physicists think the singularity represents a place where general relativity breaks down, and that a theory of quantum gravity would remove the infinities associated with the singularity--perhaps instead of being crushed to infinite density, the matter in a black hole would just be crushed to the Planck density where quantum gravitational effects are thought to become significant, and who knows what would happen at that point. This is again an issue of quantum gravity, in general relativity there would be no minimum mass, but it's thought that quantum gravity would imply that the Planck mass is the smallest possible for a black hole. This is around 10^-5 grams, about the mass of a flea--much larger than any known elementary particle.

I also did some follow-up research/reading on this topic and found some interesting theories. It seems that Brian Greene (of Columbia University) proposed that an Electron "could" be considered a miniature Black Hole given that both can be defined by mass, charge and spin. However, the problem appears to be that Hawking radiation requires such small "Black Hole" should immediately evaporate away in a shower of photons (rather than a photon). So, here's my follow-up question:
Can a Black Hole be created purely out of Energy (i.e. Photons)? On a related note, have we been able to produce Matter using only Energy as input as illustrated by Einstein's famous equation? I'm asking this question because I'm wondering if the two can represent different manifestation of similar entity (or even a symmetry that seems to be the rule in nature).
Again, what I write is purely out of speculation, so please excuse the lack of fundamental basis. Hopefully you can pass it off as an exercise in educating a newbie.

 

[jhe1984]

I wonder if Brian Greene was speaking solely in terms of the Standard Model of quantum mechanics or if it was in the context of a larger conception of the universe: such as the 11-dimensional Universe Greene and other string theorists propose. Maybe there is no distinction, but
I'd imagine that what would be considered a black hole in a 4d spacetime would look a little different in 11d.

 

[dicerandom]

Most extra-dimensional black holes (read: solutions to Einstein's Equation in higher dimensions) require that, in order for the black hole to be stable, the extra dimensions must be compactified on a length scale smaller than that of the event horizon. Therefore, to someone outside of the horizon, there's basically no difference between a black hole which is purely 4-dimensional and a black hole which has more than four dimensions.

 

[ThomasFuhlery]

Interesting. I did further research and reading into the concept of "Singularity" and found your description to be accurate. I suppose that this infinite density concept is relative to the outsider's frame of reference, so is it possible that within the Event Horizon, everything is proceeding as usual -- infiinitely collapsing towards the singularity? If so, is this not a reversed picture of our Universe expanding into infinity? Also, since the enormous gravitational curvature caused by the Black Hole can also be considered infinite, shouldn't the region inside the Event Horizon also be considered infinite as far as Space-Time goes? Assuming that's true, can Black Hole be considered a form of a sub-Universe?

This is interesting. If this were true, then could it be possible for there to exist an opposite of a black hole, and wouldn't that be what our universe is? (i.e. expanding as opposed to collapsing into infinity?) Also, why wouldn't the event horizon be infinitely large if the singularity had infinite density? is this because you can't go over a certain mass/density ratio?
Consider the possibility that if in our universe, which is expanding into infinity, there are objects in which things collapse into infinity, then within a black hole (or within the singularity) could there be an object that is expanding to infinity (only in a dimention outside of 4d)? And if that's true couldn't our entire universe exist within a singularity in 2d?

 

[masudr]

Also, why wouldn't the event horizon be infinitely large if the singularity had infinite density? is this because you can't go over a certain mass/density ratio?

This assumes some kind of linear relationship between density and event horizon. This is not the case. The spacetime around a black hole (and indeed all kinds of spacetimes we've had the chance to examine in detail) appear to be best described by what are called "Einstein's field equations" (i.e. the equations that describe General Relativity). These are a fairly complicated set of equations with very few solutions.

Luckily, assuming various symmetries, we can derive some solutions; the simplest is perhaps the Schwarzschild solution. We often use this solution (and a few others that account for spinning/charged bodies before they collapsed) to describe black holes, and the relationship between the mass (which is always finite, despite whatever the density may be) and the event horizon is:

$$r_s=\frac{2GM}{c^2}.$$