# The Unexistence of Singularity Inside the Event Horizon

All right, physicists claim that mass can be at infinite density. This condition is called the singularity, an one-dimensional point that is having mass (or energy, whatever)inside it.

I say mass cannot possibly form singularities. Why? Because of the following:

When there is mass inside a ball that has a radius of r, it seems to fill the space of 4/3 pi(=3.1415926 etc.)*r^3. But is the volume of the ball really this? Let's see. Mass makes the space twist. Now what does it mean when space bends? Let's imagine a typical picture ov mass bending the space. We see a level which is bent so that the mass in on a "hole" on the level, it is lower than the rest of the level.

Now we can see that when a flat level bents, it also stretches. And when it stretches, it gains more area. Now when we add the third dimension to this, we understand that when space bends, it gains more volume.

Thus there is a greater space inside the ball than could be guessed from outside. The radius also grows, naturally. Now if we put enough mass into this ball, it eventually forms an event horizon around itself. At this stage the space is so much bent that the radius becomes infinite. And because of that, there is also an infinite space inside every event horizon. And inside that space, somewhere, is the mass of the black hole. But because r is infinite, event horizons have no central point, and thus there cannot be a singularity.

What do you think of this?

chroot
Staff Emeritus
Gold Member
Actually, very few physicists believe in singularities. Typically, infinities indicate the failure of a model in some domain -- for example, the ultraviolet catastrophe was an infinity that resulting in the development of quantum mechanics. When infinities appear, it's usually a sign that something is in need of quantization. In the case of black holes, it is gravitation that needs to be quantized. The competing theories for this quantization are string theory and loop quantum gravity. Both promise to remove the singularity from the model.

- Warren

Hi

I think you are not able to visualise infinite density. You could imagine a region of infinite density as one where everything is on top of everything else. And it is not as u said that as the space-time is stretched, the are inceases. If u place a mass in the fabric of space-time, then the space time curves into the mass. You could expect a singularity solution for such an inward curvature, especially, when the density of the object is extremely high, like say a black hole. You could try an analogous experiment in ur house by placing a small ball in a stretched elastic sheet. You will find that if a mass is placed at the centre of the sheet, the ball circles into the mass . This experiment, though not experimentally sufficient is enough to understand the space-time curvature due to extremely dense objects.

Sridhar

Well, good if there are no singularities in mathematical sense. But i referred to singularity as a condition, where mass density is infinite. And then i wrote my opinion of the subject, why cannot such a thing take place? Answer was simplifiedly this: when the outer volume of a piece is mass is zero, great gravitation bends space, which increases the inner volume of the piece.

By the way, i apologize for all lingual mistaces I've made so far. English is not my natural language...

Originally posted by sridhar_n
I think you are not able to visualise infinite density. You could imagine a region of infinite density as one where everything is on top of everything else. And it is not as u said that as the space-time is stretched, the are inceases. If u place a mass in the fabric of space-time, then the space time curves into the mass. You could expect a singularity solution for such an inward curvature, especially, when the density of the object is extremely high, like say a black hole. You could try an analogous experiment in ur house by placing a small ball in a stretched elastic sheet. You will find that if a mass is placed at the centre of the sheet, the ball circles into the mass . This experiment, though not experimentally sufficient is enough to understand the space-time curvature due to extremely dense objects.

Sridhar

If you place a mass in the sheet, the sheet bends all right. And in the process of bending it also stretches. Now if you put a mass in space, it bends the space in its fourth dimension (space dimension, no need to get involved with time). And when the space bends, it also stretches, but in the case of space, stretching means that the volume instead of area increases. Thus in a greately curved space, the volume of a ball with diameter of d is bigger than that of the same ball in more weakly curved space.

Thus, the infinite density is not possible, because the volume grows when we increase the bending of space.

If the volume measured from outside is V and the object has some mass, the INNER volume (which is the volume we must use when we measure density) is greater than V. This phenomenon is, of course, not measurable with objects with very small masses and realtively great outer volumes. For example, the basketballs mass does not effect its volume very much. But objects with the size of Earth, for example, already notice this. The way from the surface of earth to the center of it is a few centimetres longer than the diameter/2. I don't know the exact values.

Instead of seeing the stretching of Space-Time Fabric as a whole, u could see it as n efect of force at one point, that origin if force is what we are interested, and at the point (one single point) is the effect of infinite density seen. I think u still have a problem visualising it.

Just follow the link below for a picture of space-time curvature by a mass and then i think should be able to get a clearer view of what curvature due to mass is...

http://www20.brinkster.com/starciti/curve.jpg

Sridhar

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chroot
Staff Emeritus
Gold Member
Both of you guys need to get away from the rubber-sheet analogy, because it just simply isn't right. It's an analogy, not an example of how gravity works. It's useful to help someone first get their mind around the concept that gravitation is due to curved spacetime. It is not an accurate way to model the real thing.

Real spacetime does not "stretch" in any way like a rubber sheet does. Real spacetime is curved in all four dimensions, including time, unlike the rubber sheet.

I've already answered your fundamental question, Herra. There are no real singularities, neither mathematical nor physical. They don't (and can't) really exist. Classical general relativity predicts them, so classical general relativity is wrong. A quantum gravitational theory will extend general relativity and will remove such singularities from the model by (most likely) quantizing volume.

- Warren

...

I think it would be better if we restricted our discussion with respect to Classical General Relativity. A Quantum Version has not yet been completetly framed, so why predetermine what a Theory of Quantum Gravity has to say. It has been shown that there was a singular solution to the beginning of the Universe and the singularity solution is consistent with the existing theories on the Beginning of the Universe. So I don't see any problem in the singularity solution given by Classical GR. You don't have to see singularity as a place with R = 0. R cannot be a perfect zero since space is quantized, however, you could assume a singulrity to be a really small region of space-time, probably of the order of planck length and time. So I don't think we need to wait for a theory of Quantum Gravity in order to predict/reject singularities. Singularities should exist, where else would you think can there be a better link between GR and Quantum Gravity. It is at these singularities that QM and GR meet . So why avoid them?

Sridhar

chroot
Staff Emeritus
Gold Member

Originally posted by sridhar_n
I think it would be better if we restricted our discussion with respect to Classical General Relativity.
Why would we restrict our discussion about the limits of a theory that we know is not complete to only that theory?
A Quantum Version has not yet been completetly framed, so why predetermine what a Theory of Quantum Gravity has to say.
If it still claims a singularity in the middle of a black hole, it is also not a complete theory. I've already explained that infinities in physical theories are indicators of an incomplete model.
So I don't see any problem in the singularity solution given by Classical GR.
Everyone else does.
You don't have to see singularity as a place with R = 0. R cannot be a perfect zero since space is quantized, however, you could assume a singulrity to be a really small region of space-time, probably of the order of planck length and time.
That is, by definition, NOT A SINGULARITY.
So why avoid them?
Because they are unphysical.

- Warren

The problem with (most) singularities is that our theories fail to make predictions at them: given a singular state, you can't extrapolate forward or backward to predict what will happen. Ideally, we would like laws of physics that can make predictions in any circumstance.

If it still claims a singularity in the middle of a black hole, it is also not a complete theory. I've already explained that infinities in physical theories are indicators of an incomplete model.

The problem with (most) singularities is that our theories fail to make predictions at them: given a singular state, you can't extrapolate forward or backward to predict what will happen. Ideally, we would like laws of physics that can make predictions in any circumstance.

The laws of physics are not to be custom made. If there is singularity in nature, then we have to accept it. The laws of Physics are meant to tell u what is there around you and not what should be there...

You don't have to see singularity as a place with R = 0. R cannot be a perfect zero since space is quantized, however, you could assume a singulrity to be a really small region of space-time, probably of the order of planck length and time. - That is, by definition, NOT A SINGULARITY.

Well we have something called tending towards a value. And we also know that one cannot reach absolute zero and there is a definite limit to all our observations. So instead of looking for a zero valued singularity, why can't we use the smallest possible distance as singularity? This is what I meant.

So I think it would be better if the laws of Physics would better explain what is actually around us than what we expect should be happening around us. If u feel that something that is actually there is mathematically confusing, u have to accept it that way. You can't help it. You just can't design Nature the way that u want it to be. You have to accept facts.

Sridhar

chroot
Staff Emeritus
Gold Member
Originally posted by sridhar_n
The laws of physics are not to be custom made. If there is singularity in nature, then we have to accept it. The laws of Physics are meant to tell u what is there around you and not what should be there...
There is absolutely no evidence that singularities exist in nature. What makes you think they do? We have loads of experience that demonstrate that singularities do not really exist, and are only artifacts of an incomplete model. I've said all this already -- why don't you understand it?
Well we have something called tending towards a value. And we also know that one cannot reach absolute zero and there is a definite limit to all our observations. So instead of looking for a zero valued singularity, why can't we use the smallest possible distance as singularity? This is what I meant.
The "smallest possible distance" is again, NOT A SINGULARITY. Zero radius and infinite density, to give two examples, ARE. Do you not see that there is a world of difference between "really small" and "zero?" How about between "really big" and "infinite?"
So I think it would be better if the laws of Physics would better explain what is actually around us than what we expect should be happening around us.
We do our best.
If u feel that something that is actually there is mathematically confusing, u have to accept it that way. You can't help it. You just can't design Nature the way that u want it to be. You have to accept facts.
No one is designing Nature -- what the hell are you talking about? If anything, the admission that singularities are unphysical is the ultimate physical sacrifice -- we admit that singularities don't really exist in the universe, and thus our models are at best incomplete. You seem to be arguing with me, even as we do exactly as you'd have us do.

- Warren

Can I get one proof that singularity solutions are incomplete?

Sridhar

Ok Chroot I agree...

Sridhar