# Are black holes a point of singularity?

1. Jun 15, 2010

### zewpals

Are black holes a point of singularity of infinite density, approaching that point as a limit, or just really massive and really dense?

Is light really being "sucked in" by the gravity and actually being attracted to the object, or is it really just following the really really steep bend in space-time that goes towards the black hole, and since time is so incredibly "slow" in black holes compared to Earth time, the light doesn't appear to come out because it is moving at such slow speeds? I might have just explained why it is being sucked in haha.

Also...could it be possible that Inside black holes, all four forces are actually one? If the gravity is strong enough to rip atom from atom (electromagnetic) and proton from proton (nuclear), couldn't it be strong enough to assimilate all four forces? We talk about speed and heat being the only ways to mimic the beginning of time. How about a large amount of gravity?

Off topic: The Big Bang might have been a black hole that disintegrated, eh?

2. Jun 15, 2010

### Angry Citizen

As far as I'm aware, black holes are singularities of infinite density, and the 'simple' ones that don't rotate act as a point -- a geometric point, mind you, meaning possessing zero dimensions.

General relativity states that light is being bent by the curvature of space-time. Once light passes the event horizon, all possible paths out of the black hole turn in on itself. In other words, imagine a giant, impenetrable barrier. There's simply no way out of a black hole once you're in.

We really don't know what happens when you're 'inside' a black hole. That's the problem. Various silly theories like string theory continue to become more and more complicated, but I doubt we're any closer to discovering the 'theory of everything', which is likely heralded by a theory of quantum gravity (note that this is so important to black holes because quantum mechanics deals with the very very small, and the only thing that possesses lots and lots of gravity while still being very very small [in fact, infinitely small] is a black hole).

Personally, I think we're still in a black hole. I don't think the singularity ever disintegrated. But what do I know, I'm just a well-read engineering student.

3. Jun 15, 2010

### zewpals

Ah thank you! That cleared up a bit. The one thing I am a little on the edge about is grasping my mind around is the point of singularity. Each black hole as its own unique mass, so each point of singularity has it's own unique mass, yet each one has an infinite density. I guess they could only be a point in space and time if there is no physical matter (i.e. protons and sub atomic particles) and all forces could be one.

I did read some where that black holes are supposed to be "a few kilometers wide" is that talking about event horizon, or was the author misinformed?

I'm a not-so-well-read bioengineering student, so my guess is as viable as a toddler trying to answer calculus questions. However, I did think about this before you posted it and refuted it because we can break down the universe into multiple parts. It isn't just "one". But at the same time, it kind of is just "one", because that's the way the universe probably started. I really think that the black hole that could have been before the beginning of our universe decayed, and the dark energy caused the hyper inflation, releasing everything from that one point to become four forces and matter.

again, i have no authority making any actual hypothesis haha

4. Jun 15, 2010

### Angry Citizen

Imagine it like this. Every black hole is theoretically unique only in its mass, its charge, and its angular momentum (AKA rotation). But the thing that matters most is its mass.

Fundamentally, a black hole is no different than any other mass. If the sun were to spontaneously turn into a black hole right now, the Earth would continue orbiting as though nothing had ever happened (although it'd get a little chilly). What's different about a black hole is its density. You can get inside the sun, and the gravity's going to be fairly large, but light can easily escape it. But crossing 'into' a black hole just means crossing the barrier at which gravity becomes so large that light is unable to escape. Since gravity is classically defined as an inverse square force, that means that distance decreases the gravitic force by its square; consequently, it takes a correspondingly larger amount of mass to have the same effect at, say, 50 miles from the center as it would 25 miles from the center. To wrap this convoluted explanation together, the more mass a black hole has, the greater its gravity, and the farther it can extend the unique property of 'capturing' light -- also known as the event horizon.

Thus, a black hole the size of the Earth might have an event horizon diameter of a few meters. A black hole the size of a million billion suns might have an event horizon diameter of Saturn's orbit, or something similarly large (I'm not familiar with the calculations necessary -- again, just a humble engineering student).

5. Jun 15, 2010

### zewpals

Alright, GREAT thanks a lot.

6. Jun 15, 2010

### cepheid

Staff Emeritus
Well here's a calculation that any humble engineering student should be able to understand. It relies solely on Newtonian gravitation (no GR). To calculate the radius inside of which light cannot escape, all you have to do is figure out the radius at which the escape velocity is equal to c. To do this, note that in order for a test particle of mass m to escape from a black hole of mass M when it starts at a distance R away from it, its kinetic energy must be equal in magnitude to its gravitational potential energy. The argument is as follows: by convention the gravitational potential energy of this two particle system is set to zero "at infinity", so the gravitational potential energy that was lost by the test mass moving (conceptually) into the potential well from infinity to a radius R is equal to the energy the particle needs to get back out of the well, i.e. to escape to infinity. If the particle has less kinetic energy than that, then as it moves away from the black hole, its kinetic energy will decrease and will reach zero at some finite radius. Therefore, the particle will fall back into the well. So, with this condition that the kinetic energy must be equal in absolute value to the gravitational potential energy, we have the relation:

$$\frac{1}{2}mv^2 = G\frac{Mm}{R}$$

$$\frac{1}{2}v^2 = \frac{GM}{R}$$​

Setting the escape velocity equal to c:

$$c^2 = 2\frac{GM}{R}$$

$$R_s = 2\frac{GM}{c^2}$$​

In the last step I've called the radius Rs, because this is the Schwarzchild radius of a black hole. Believe it or not, this analysis, as sketchy as it seems, gives you the right answer (i.e. the expression for the Schwarzchild radius derived from General Relativity is the same). The big difference in GR is that the black hole has an event horizon with radius Rs -- we can never learn anything about the events taking place within this region. Doing so would require information to travel faster than the speed of light, which it cannot in GR (if it could, then it would be possible to violate causality).

Using this formula, an Earth mass black hole has a Schwarzchild radius of 8.87 mm.

A 1015 $\textrm{M}_\odot$ black hole (which, by the way, is ridiculous even for a supermassive black hole) would have a Schwarzchild radius of 95 parsecs, or 19,742,459 AU. For reference, the diameter of Saturn's orbit is about 19 AU, so your estimate was only 6 orders of magnitude too small. :tongue2:

7. Jun 16, 2010

### Chronos

Agreed, cepheid. Our limit of detectability for any black hole is its event horizon. What occurs within is unobservable. It is unclear if a true singularity ever actually forms.

8. Jun 16, 2010

### zewpals

Thanks cepheid, the math helped me out. I would imagine it would be much easier to detect black holes (just because there would be nothing in that area of the celestial background) if other masses did not warp and distort light around them.

9. Jun 16, 2010

### Calluuuum

I believe this would just be because you're trying to divide a mass by a volume of 0. A singularity is just where the mass all converges into a point with 0 volume and therefore infinite density (put simply). No matter what mass you're dividing, it's still divided by 0 which is infinite. Remember, density is simply mass over volume.

10. Jun 16, 2010

### zewpals

Haha yeah I understand that. Actually, since density is mass/volume, if a body was 2 dimensional or 1-dimensional, wouldn't it also have an infinite density?

11. Jun 16, 2010

### Angry Citizen

Yes. And that's why a rotating black hole is still a black hole of infinite density, despite the fact that its singularity is supposed to be one dimensional (I.E. a line).

12. Jun 16, 2010

### zewpals

Wow! I thought it was zeroth dimensional! How could it be a "singularity" if it's more than one point though?

13. Jun 16, 2010

### Angry Citizen

Rotation causes the singularity to stretch to the 1st dimension. 0th dimension black holes only exist as stationary, non-rotating entities.

And of course, I should note that this talk of dimensions is all quite theoretical. As I mentioned, we really don't know what goes on inside a black hole. But all this talk of 0th dimension singularities and single dimension singularities comes straight from general relativity, which may or may not be accurate at the quantum level.

14. Jun 16, 2010

### zewpals

Alright, thanks for clarifying that; that was very helpful.

Hmm...assuming the theory that the universe started as a point of singularity is correct...I wonder if it rotated due to some internal inertia, and if so I wonder if inflation only occurred because of that rotation and inertia. haha time for a new thread!