Can a singularity be reached?

[dstebbins]

It is generally accepted among astronomers that the heart of a black hole, the singularity, is an infinitely small geometric point, of infinit gravity and infinite density. It is derived through theoretical physics that at this singularity, space and time come to a screetching hault, and everything that reaches it is crushed out of existence.

 

Or is it?

 

Aproximately a century ago, Albert Einstein suggested in the theory of relativity that the force of gravity acted, not on objects, but on spacetime, curving it, and objects and energy just follow the curved path.

 

So, by that logic, if the singularity is of infinite gravity, then spacetime must be infinitely distorted. Therefore, as an object were to fall into a black hole, it should freefall indefinately because spacetime is curved indefinately, and therefore never reaches the singularity. It falls and falls and falls until the black hole eventually evaporates. That's why we would never see an object pass through a black hole, because it doesn't pass through. It just falls indefinately, and it appears to come to a stop near the center because the dimension of time is distorted so severely that it goes by at a negligible rate. If we were to sit there and watch for years and years, it would slowly move according to our vision, getting closer and closer to the heart of the black hole, but never reaches it, much like how the graph of xy = 1 gets closer and closer to the axes, but never touch.

 

Gentlemen, I'll take your questions now!

[ajb]

No body thinks that we have infinite curvature in a black hole. It is just showing the break down of general relativity and telling us that we need some new physics.

 

Throughout the development of modern physics the presence of infinities has lead to new developments. For example, the electron's self energy led to quantum field theory. Why should we expect any difference in general relativity?

 

Most people think that on the small scale general relativity will no longer hold and that some quantum theory of gravity will "smooth out" the infinite curvature.

 

We also have time dilation effects to take into account as a distant observer. We never see the particle cross the event horizon. Time dilation effects means that from our point of view, it takes infinite time for the particle to reach the event horizon. (again another infinity, new physics?) But as far as the particle is concerned, it does cross the event horizon in finite time. So you need to make your statments more precise and state which observer you are talking about.

[dstebbins]

No body thinks that we have infinite curvature in a black hole. It is just showing the break down of general relativity and telling us that we need some new physics.

 

Throughout the development of modern physics the presence of infinities has lead to new developments. For example, the electron's self energy led to quantum field theory. Why should we expect any difference in general relativity?

 

Most people think that on the small scale general relativity will no longer hold and that some quantum theory of gravity will "smooth out" the infinite curvature.

 

We also have time dilation effects to take into account as a distant observer. We never see the particle cross the event horizon. Time dilation effects means that from our point of view, it takes infinite time for the particle to reach the event horizon. (again another infinity, new physics?) But as far as the particle is concerned, it does cross the event horizon in finite time. So you need to make your statments more precise and state which observer you are talking about.

 

So, what you're trying to say in the fewest words possible is that General Relativity is being replaced with other, more universal (no pun intended) physics?

[ajb]

So, what you're trying to say in the fewest words possible is that General Relativity is being replaced with other, more universal (no pun intended) physics?

 

Yes, on small scales (high energy) gravity will need to be explained in some quantum frame work. This will presumably, get rid of the infinite curvature.

 

The point of my post is that you have top be careful trying to extract "physics" from infinities. Infinite curvature is a signiture of general relativity failing on some scale. So I would be very careful about trying to attatch real physics to this near or at this singularity.

 

I also think (within general relativity) you have to be clear about if you are talking about "naked" singularities or hidden ones. As an outside observer we never see the singularity inside a black hole, it it hidden from us by the event horizon. Also if we send a probe towards the event horizon we never see it reach the horizon, although from the probes point of view it does cross the horizon. So, in some sence what you said is correct, we never see anything passing through the blackhole. Of course, there are huge tidal forces near the singularity that will rip apart our probe, but we will never know about it.

 

As for naked singularites (if they are possible in GR) I don't know. As these don't have event horizons maybe we can see a little more? See what google says!

[lakmilis]

I agree with what you say ajb, but I am not sure if I would say 'nobody' thinks we have infinite curvature.... why not? 1/0 is an infinity, but do we say division is meaningless...can we exctract any information about the special case n/0, sure.

 

What is so factual conceptually with it not being able to be infinite? This layman popular way of everyone being space-time understanders of using D-1 dimensions in visualising curvature of space?

 

I say I am happy to think the singularity is indeed an infinite curvature till theories meet each other enough to prove elsewise.

[ajb]

[math] 1/ 0[/math] is not infinity, it is undefined. [math] lim_{x\rightarrow 0}\frac{1}{x}[/math] is infinity.

 

Infinities are just difficult things to think about and don't seem very natural. How would you measure an infinite quantity, what does a quantity being infinite physically mean?

 

One should be careful about mathematical infinities in a theory and physical infinities in nature. No example of the latter has ever been found.

[lakmilis]

sorry about that ajb, I merely used the most banal example, I know the definition, but in maths we do set the undefined as either boundary conditions or express them as well as infinites.

 

Alas, in physics we have never found infinites? yes, singularities...hehe yes I know what you mean...But I just still am not willing to accept this inductive step that since we know not of infinites within the universe, that singularities are not either.

 

I have a notion of black holes spinning at the speed of light... this would entail infinite curvature....or conversely, if there is an infinite curvature, they must spin at the speed of light...

 

(just a notion, not stating this as fact...just want to show why I say I do not yet wanna reject the idea )

 

(oh , hehe and this is gonna might frustrate ya because I know this is just a metaphysical statement until provable?, but lets say I claimed a/the 4th dimension is actually a/the physical infinity) But ye last part is not really a part of the topic, sorry

[ajb]

I know the definition, but in maths we do set the undefined as either boundary conditions or express them as well as infinites.

 

I am not sure what you mean by this, but never mind.

 

Alas, in physics we have never found infinites? yes, singularities...hehe yes I know what you mean...But I just still am not willing to accept this inductive step that since we know not of infinites within the universe, that singularities are not either.

 

Isn't a singularity defined as a point of infinite curvature? I think the two notions of singularity and infinity are equivalent in this set-up.

 

 

I have a notion of black holes spinning at the speed of light... this would entail infinite curvature....or conversely, if there is an infinite curvature, they must spin at the speed of light...

 

Examine the Kerr metric (and maybe other solutions) and see what happens.

[lakmilis]

1st reply, yup nvm

2nd reply, yup, I agree

3rd reply. Yup, I see the Kerr metric as the viable one for existing black holes, not the Schw. metric

[lakmilis]

oh and stebbins, the falling indefinitely is the same as when I used to tell young peeps that no circles have centres...leading into all objects converge into a obcect-dimensionality+1 aka the 4th dimension. Like all finite objects converge into infinity etc

 

just to whop out an idea hihi

[etrader]

I think this discussion is in vain

 

Singularity is the key for everything as claimed by theoretical physicists.

 

If it really exists, we can have the so-called theory of everything. Then, ...

 

Since this claim, it was the subject of debate between the greatest scientists of our time, but no convinving result up to now, just discussions.

[ajb]

I think this discussion is in vain

 

Singularity is the key for everything as claimed by theoretical physicists.

 

If it really exists, we can have the so-called theory of everything. Then, ...

 

 

You will have to explain these remarks.

[Royston]

I think this discussion is in vain

 

Singularity is the key for everything as claimed by theoretical physicists.

 

If it really exists, we can have the so-called theory of everything. Then, ...

 

Since this claim, it was the subject of debate between the greatest scientists of our time, but no convinving result up to now, just discussions.

 

I think what you mean to say is, 'a resolution to the singularity problem has been discussed (it's been more than 'discussed' anyway) but with no convincing results'...you need to cite sources if you're going to make claims like the above.